3.3.1 Parallel sparse direct solvers

For the solution of large sparse linear systems, we design numerical schemes and software packages for direct and hybrid parallel solvers. Sparse direct solvers are mandatory when the linear system is very ill-conditioned; such a situation is often encountered in structural mechanics codes, for example. Therefore, to obtain an industrial software tool that must be robust and versatile, high-performance sparse direct solvers are mandatory, and parallelism is then necessary for reasons of memory capability and acceptable solution time. Moreover, in order to solve efficiently 3D problems with more than 50 million unknowns, which is now a reachable challenge with new multicore supercomputers, we must achieve good scalability in time and control memory overhead. Solving a sparse linear system by a direct method is generally a highly irregular problem that induces some challenging algorithmic problems and requires a sophisticated implementation scheme in order to fully exploit the capabilities of modern supercomputers.

New supercomputers incorporate many microprocessors which are composed of one or many computational cores. These new architectures induce strongly hierarchical topologies. These are called NUMA architectures. In the context of distributed NUMA architectures, in collaboration with the Inria STORM team, we study optimization strategies to improve the scheduling of communications, threads and I/O. We have developed dynamic scheduling designed for NUMA architectures in the PaStiX solver. The data structures of the solver, as well as the patterns of communication have been modified to meet the needs of these architectures and dynamic scheduling. We are also interested in the dynamic adaptation of the computation grain to use efficiently multi-core architectures and shared memory. Experiments on several numerical test cases have been performed to prove the efficiency of the approach on different architectures. Sparse direct solvers such as PaStiX are currently limited by their memory requirements and computational cost. They are competitive for small matrices but are often less efficient than iterative methods for large matrices in terms of memory. We are currently accelerating the dense algebra components of direct solvers using block low-rank compression techniques.

In collaboration with the ICL team from the University of Tennessee, and the STORM team from Inria, we are evaluating the way to replace the embedded scheduling driver of the PaStiX solver by one of the generic frameworks, PaRSEC or StarPU, to execute the task graph corresponding to a sparse factorization. The aim is to design algorithms and parallel programming models for implementing direct methods for the solution of sparse linear systems on emerging computer equipped with GPU accelerators. More generally, this work will be performed in the context of the ANR SOLHARIS project which aims at designing high performance sparse direct solvers for modern heterogeneous systems. This ANR project involves several groups working either on the sparse linear solver aspects (HiePACS and ROMA from Inria and APO from IRIT), on runtime systems (STORM from Inria) or scheduling algorithms (HiePACS and ROMA from Inria). The results of these efforts will be validated in the applications provided by the industrial project members, namely CEA-CESTA and Airbus Central R & T.

3.3.2 Hybrid direct/iterative solvers based on algebraic domain decomposition techniques

One route to the parallel scalable solution of large sparse linear systems in parallel scientific computing is the use of hybrid methods that hierarchically combine direct and iterative methods. These techniques inherit the advantages of each approach, namely the limited amount of memory and natural parallelization for the iterative component and the numerical robustness of the direct part. The general underlying ideas are not new since they have been intensively used to design domain decomposition techniques; those approaches cover a fairly large range of computing techniques for the numerical solution of partial differential equations (PDEs) in time and space. Generally speaking, it refers to the splitting of the computational domain into sub-domains with or without overlap. The splitting strategy is generally governed by various constraints/objectives but the main one is to express parallelism. The numerical properties of the PDEs to be solved are usually intensively exploited at the continuous or discrete levels to design the numerical algorithms so that the resulting specialized technique will only work for the class of linear systems associated with the targeted PDE.

In that context, we continue our effort on the design of algebraic non-overlapping domain decomposition techniques that rely on the solution of a Schur complement system defined on the interface introduced by the partitioning of the adjacency graph of the sparse matrix associated with the linear system. Although it is better conditioned than the original system the Schur complement needs to be precondition to be amenable to a solution using a Krylov subspace method. Different hierarchical preconditioners will be considered, possibly multilevel, to improve the numerical behaviour of the current approaches implemented in our software library MaPHyS. This activity will be developed further developped in the H2020 EoCoE2 project. In addition to this numerical studies, advanced parallel implementation will be developed that will involve close collaborations between the hybrid and sparse direct activities.

3.3.3 Linear Krylov solvers

Preconditioning is the main focus of the two activities described above. They aim at speeding up the convergence of a Krylov subspace method that is the complementary component involved in the solvers of interest for us. In that framework, we believe that various aspects deserve to be investigated; we will consider the following ones:

• Preconditioned block Krylov solvers for multiple right-hand sides. In many large scientific and industrial applications, one has to solve a sequence of linear systems with several right-hand sides given simultaneously or in sequence (radar cross section calculation in electromagnetism, various source locations in seismic, parametric studies in general, ...). For “simultaneous" right-hand sides, the solvers of choice have been for years based on matrix factorizations as the factorization is performed once and simple and cheap block forward/backward substitutions are then performed. In order to effectively propose alternative to such solvers, we need to have efficient preconditioned Krylov subspace solvers. In that framework, block Krylov approaches, where the Krylov spaces associated with each right-hand side are shared to enlarge the search space will be considered. They are not only attractive because of this numerical feature (larger search space), but also from an implementation point of view. Their block-structures exhibit nice features with respect to data locality and re-usability that comply with the memory constraint of multicore architectures. We will continue the numerical study and design of the block GMRES variant that combines inexact break-down detection, deflation at restart and subspace recycling. Beyond new numerical investigations, a software implementation to be included in our linear solver libray Fabulous originately developed in the context of the DGA HiBox project and further developped in the LynCs (Linear Algebra, Krylov-subspace methods, and multi-grid solvers for the discovery of New Physics) sub-project of Prace-6IP.
• Extension or modification of Krylov subspace algorithms for multicore architectures: finally to match as much as possible to the computer architecture evolution and get as much as possible performance out of the computer, a particular attention will be paid to adapt, extend or develop numerical schemes that comply with the efficiency constraints associated with the available computers. Nowadays, multicore architectures seem to become widely used, where memory latency and bandwidth are the main bottlenecks; investigations on communication avoiding techniques will be undertaken in the framework of preconditioned Krylov subspace solvers as a general guideline for all the items mentioned above.

3.3.4 Eigensolvers

Many eigensolvers also rely on Krylov subspace techniques. Naturally some links exist between the Krylov subspace linear solvers and the Krylov subspace eigensolvers. We plan to study the computation of eigenvalue problems with respect to the following two different axes:

• Exploiting the link between Krylov subspace methods for linear system solution and eigensolvers, we intend to develop advanced iterative linear methods based on Krylov subspace methods that use some spectral information to build part of a subspace to be recycled, either though space augmentation or through preconditioner update. This spectral information may correspond to a certain part of the spectrum of the original large matrix or to some approximations of the eigenvalues obtained by solving a reduced eigenproblem. This technique will also be investigated in the framework of block Krylov subspace methods.
• In the context of the calculation of the ground state of an atomistic system, eigenvalue computation is a critical step; more accurate and more efficient parallel and scalable eigensolvers are required.

3.3.5 Fast Solvers for FEM/BEM Coupling

In this research project, we are interested in the design of new advanced techniques to solve large mixed dense/sparse linear systems, the extensive comparison of these new approaches to the existing ones, and the application of these innovative ideas on realistic industrial test cases in the domain of aeroacoustics (in collaboration with Airbus Central R & T).

• The use of $\mathscr{H}$-matrix solvers on these problems has been investigated in the context of the PhD of A. Falco. Airbus CR&T, in collaboration with Inria Bordeaux Sud-Ouest, has developed a task-based $\mathscr{H}$-matrix solver on top of the runtime engine StarPU. Ideas coming from the field of sparse direct solvers (such as nested dissection or symbolic factorization) have been tested within $\mathscr{H}$-matrices.
• The question of parallel scalability of task-based tools is an active subject of research, using new communication engine such as NewMadeleine, that will be investigated during this project, in conjunction with new algorithmic ideas on the task-based writing of $\mathscr{H}$-matrix algorithms.
• Naturally, comparison with existing tools will be performed on large realistic test cases. Coupling schemes between these tools and the hierarchical methods used in $\mathscr{H}$-matrix will be developed and benched as well.

3.4.1 Improvement of calculation efficiency

Nowadays, the high performance computing community is examining alternative architectures that address the limitations of modern cache-based designs. GPU (Graphics Processing Units) and the Cell processor have thus already been used in astrophysics and in molecular dynamics. The Fast Mutipole Method has also been implemented on GPU. We intend to examine the potential of using these forthcoming processors as a building block for high-end parallel computing in N-body calculations. More precisely, we want to take advantage of our specific underlying BLAS routines to obtain an efficient and easily portable FMM for these new architectures. Algorithmic issues such as dynamic load balancing among heterogeneous cores will also have to be solved in order to gather all the available computation power. This research action will be conduced on close connection with the activity described in Section 3.2.

3.4.2 Non uniform distributions

In many applications arising from material physics or astrophysics, the distribution of the data is highly non uniform and the data can grow between two time steps. As mentioned previously, we have proposed a hybrid MPI-thread algorithm to exploit the data locality within each node. We plan to further improve the load balancing for highly non uniform particle distributions with small computation grain thanks to dynamic load balancing at the thread level and thanks to a load balancing correction over several simulation time steps at the process level.

3.4.3 Fast multipole method for dislocation operators

The engine that we develop will be extended to new potentials arising from material physics such as those used in dislocation simulations. The interaction between dislocations is long ranged ($O(1/r)$) and anisotropic, leading to severe computational challenges for large-scale simulations. Several approaches based on the FMM or based on spatial decomposition in boxes are proposed to speed-up the computation. In dislocation codes, the calculation of the interaction forces between dislocations is still the most CPU time consuming. This computation has to be improved to obtain faster and more accurate simulations. Moreover, in such simulations, the number of dislocations grows while the phenomenon occurs and these dislocations are not uniformly distributed in the domain. This means that strategies to dynamically balance the computational load are crucial to achieve high performance.

3.4.4 Fast multipole method for boundary element methods

The boundary element method (BEM) is a well known solution of boundary value problems appearing in various fields of physics. With this approach, we only have to solve an integral equation on the boundary. This implies an interaction that decreases in space, but results in the solution of a dense linear system with $O\left(N^3\right)$ complexity. The FMM calculation that performs the matrix-vector product enables the use of Krylov subspace methods. Based on the parallel data distribution of the underlying octree implemented to perform the FMM, parallel preconditioners can be designed that exploit the local interaction matrices computed at the finest level of the octree. This research action will be conduced on close connection with the activity described in Section 3.3. Following our earlier experience, we plan to first consider approximate inverse preconditionners that can efficiently exploit these data structures.

3.5.1 Dynamic load-balancing with variable number of processors

As a preliminary step related to the dynamic load balancing of coupled codes, we focus on the problem of dynamic load balancing of a single parallel code, with variable number of processors. Indeed, if the workload varies drastically during the simulation, the load must be redistributed regularly among the processors. Dynamic load balancing is a well studied subject but most studies are limited to an initially fixed number of processors. Adjusting the number of processors at runtime allows one to preserve the parallel code efficiency or keep running the simulation when the current memory resources are exceeded. We call this problem, MxN graph repartitioning.

We propose some methods based on graph repartitioning in order to re-balance the load while changing the number of processors. These methods are split in two main steps. Firstly, we study the migration phase and we build a “good” migration matrix minimizing several metrics like the migration volume or the number of exchanged messages. Secondly, we use graph partitioning heuristics to compute a new distribution optimizing the migration according to the previous step results.

3.5.2 Load balancing of coupled codes

As stated above, the load balancing of coupled code is a major issue, that determines the performance of the complex simulation, and reaching high performance can be a great challenge. In this context, we develop new graph partitioning techniques, called co-partitioning. They address the problem of load balancing for two coupled codes: the key idea is to perform a "coupling-aware" partitioning, instead of partitioning these codes independently, as it is classically done. More precisely, we propose to enrich the classic graph model with inter-edges, which represent the coupled code interactions. We describe two new algorithms, and compare them to the naive approach. In the preliminary experiments we perform on synthetically-generated graphs, we notice that our algorithms succeed to balance the computational load in the coupling phase and in some cases they succeed to reduce the coupling communications costs. Surprisingly, we notice that our algorithms do not degrade significantly the global graph edge-cut, despite the additional constraints that they impose.

Besides this, our co-partitioning technique requires to use graph partitioning with fixed vertices, that raises serious issues with state-of-the-art software, that are classically based on the well-known recursive bisection paradigm (RB). Indeed, the RB method often fails to produce partitions of good quality. To overcome this issue, we propose a new direct $k$-way greedy graph growing algorithm, called KGGGP, that overcomes this issue and succeeds to produce partition with better quality than RB while respecting the constraint of fixed vertices. Experimental results compare KGGGP against state-of-the-art methods, such as Scotch, for real-life graphs available from the popular DIMACS'10 collection.

3.5.3 Load balancing strategies for hybrid sparse linear solvers

Graph handling and partitioning play a central role in the activity described here but also in other numerical techniques detailed in sparse linear algebra Section. The Nested Dissection is now a well-known heuristic for sparse matrix ordering to both reduce the fill-in during numerical factorization and to maximize the number of independent computation tasks. By using the block data structure induced by the partition of separators of the original graph, very efficient parallel block solvers have been designed and implemented according to super-nodal or multi-frontal approaches. Considering hybrid methods mixing both direct and iterative solvers such as MaPHyS, obtaining a domain decomposition leading to a good balancing of both the size of domain interiors and the size of interfaces is a key point for load balancing and efficiency in a parallel context.

We intend to revisit some well-known graph partitioning techniques in the light of the hybrid solvers and design new algorithms to be tested in the Scotch package.

4.2.1 High performance simulation for ITER tokamak

Scientific simulation for ITER tokamak modeling provides a natural bridge between theory and experimentation and is also an essential tool for understanding and predicting plasma behavior. Recent progresses in numerical simulation of fine-scale turbulence and in large-scale dynamics of magnetically confined plasma have been enabled by access to petascale supercomputers. These progresses would have been unreachable without new computational methods and adapted reduced models. In particular, the plasma science community has developed codes for which computer runtime scales quite well with the number of processors up to thousands cores. The research activities of HiePACS concerning the international ITER challenge have started in the Inria Project Lab C2S@Exa in collaboration with CEA-IRFM and were related to two complementary studies: a first one concerning the turbulence of plasma particles inside a tokamak (in the context of GYSELA code) and a second one concerning the MHD instability edge localized modes (in the context of JOREK code). The activity concerning GYSELA was completed at the end of 2018.

Other numerical simulation tools designed for the ITER challenge aim at making a significant progress in understanding active control methods of plasma edge MHD instability Edge Localized Modes (ELMs) which represent a particular danger with respect to heat and particle loads for Plasma Facing Components (PFC) in the tokamak. The goal is to improve the understanding of the related physics and to propose possible new strategies to improve effectiveness of ELM control techniques. The simulation tool used (JOREK code) is related to non linear MHD modeling and is based on a fully implicit time evolution scheme that leads to 3D large very badly conditioned sparse linear systems to be solved at every time step. In this context, the use of PaStiX library to solve efficiently these large sparse problems by a direct method is a challenging issue.

This activity continues within the context of the EoCoE2 project, in which the PaStiX solver is identified to allow the processing of very larger linear systems for the nuclear fusion code TOKAM3X from CEA-IRFM. Contrary to the JOREK code, the problem to be treated corresponds to the complete 3D volume of the plasma torus. The objective is to be competitive, for complex geometries, compared to an Algebraic MultiGrid approach designed by one partner of EoCoE2.

4.2.2 Numerical and parallel scalable hybrid solvers in large scale calculations

Parallel and numerically scalable hybrid solvers based on a fully algebraic coarse space correction have been theoretically studied and various advanced parallel implementations have been designed. Their parallel scalability has been initially investigated on large scale problems within the EoCoE project thanks to a close collaboration with the BSC and the integration of MaPHyS within the Alya software. This activity will further develop in the EoCoE2 project. The performance has also been assessed on PRACE Tier-0 machine within a PRACE Project Access through a collaboration with CERFACS and Laboratoire de Physique des Plasmas at Ecole Polytechnique for the calculation of plasma propulsion. A comparative parallel scalability study with the Algebraic MultiGrid from Petsc has been conducted in that framework.

6.1.1 AVCI

• Name:
  Adaptive vibrational configuration interaction
• Keywords:
  Vibrational spectra, Eigen value
• Functional Description:

  A-VCI is a theoretical vibrational spectroscopy algorithm developed to effectively reduce the number of vibrational states used in the configuration-interaction (CI) process. It constructs a nested basis for the discretization of the Hamiltonian operator inside a large CI approximation space and uses an a-posteriori error estimator (residue) to select the most relevant directions to expand the discretization space.

  The Hamiltonian operator consists of 3 operators: a harmonic oscillator sum, the potential energy surface operator and the Coriolis operators. In addition, the code can compute the intensity of eigenvectors.

  The code can handle molecules up to 10 atoms, which corresponds to solving an eigenvalue problem in a 24-dimensional space.

• Publications:
  hal-01310708, hal-02518243, hal-01534134, hal-02524533
• Author:
  Olivier Coulaud
• Contact:
  Olivier Coulaud
• Partner:
  IPREM

6.1.2 Chameleon

• Keywords:
  Runtime system, Task-based algorithm, Dense linear algebra, HPC, Task scheduling
• Scientific Description:

  Chameleon is part of the MORSE (Matrices Over Runtime Systems @ Exascale) project. The overall objective is to develop robust linear algebra libraries relying on innovative runtime systems that can fully benefit from the potential of those future large-scale complex machines.

  We expect advances in three directions based first on strong and closed interactions between the runtime and numerical linear algebra communities. This initial activity will then naturally expand to more focused but still joint research in both fields.

  1. Fine interaction between linear algebra and runtime systems. On parallel machines, HPC applications need to take care of data movement and consistency, which can be either explicitly managed at the level of the application itself or delegated to a runtime system. We adopt the latter approach in order to better keep up with hardware trends whose complexity is growing exponentially. One major task in this project is to define a proper interface between HPC applications and runtime systems in order to maximize productivity and expressivity. As mentioned in the next section, a widely used approach consists in abstracting the application as a DAG that the runtime system is in charge of scheduling. Scheduling such a DAG over a set of heterogeneous processing units introduces a lot of new challenges, such as predicting accurately the execution time of each type of task over each kind of unit, minimizing data transfers between memory banks, performing data prefetching, etc. Expected advances: In a nutshell, a new runtime system API will be designed to allow applications to provide scheduling hints to the runtime system and to get real-time feedback about the consequences of scheduling decisions.

  2. Runtime systems. A runtime environment is an intermediate layer between the system and the application. It provides low-level functionality not provided by the system (such as scheduling or management of the heterogeneity) and high-level features (such as performance portability). In the framework of this proposal, we will work on the scalability of runtime environment. To achieve scalability it is required to avoid all centralization. Here, the main problem is the scheduling of the tasks. In many task-based runtime environments the scheduler is centralized and becomes a bottleneck as soon as too many cores are involved. It is therefore required to distribute the scheduling decision or to compute a data distribution that impose the mapping of task using, for instance the so-called “owner-compute” rule. Expected advances: We will design runtime systems that enable an efficient and scalable use of thousands of distributed multicore nodes enhanced with accelerators.

  3. Linear algebra. Because of its central position in HPC and of the well understood structure of its algorithms, dense linear algebra has often pioneered new challenges that HPC had to face. Again, dense linear algebra has been in the vanguard of the new era of petascale computing with the design of new algorithms that can efficiently run on a multicore node with GPU accelerators. These algorithms are called “communication-avoiding” since they have been redesigned to limit the amount of communication between processing units (and between the different levels of memory hierarchy). They are expressed through Direct Acyclic Graphs (DAG) of fine-grained tasks that are dynamically scheduled. Expected advances: First, we plan to investigate the impact of these principles in the case of sparse applications (whose algorithms are slightly more complicated but often rely on dense kernels). Furthermore, both in the dense and sparse cases, the scalability on thousands of nodes is still limited, new numerical approaches need to be found. We will specifically design sparse hybrid direct/iterative methods that represent a promising approach.

  Overall end point. The overall goal of the MORSE associate team is to enable advanced numerical algorithms to be executed on a scalable unified runtime system for exploiting the full potential of future exascale machines.

• Functional Description:
  Chameleon is a dense linear algebra software relying on sequential task-based algorithms where sub-tasks of the overall algorithms are submitted to a Runtime system. A Runtime system such as StarPU is able to manage automatically data transfers between not shared memory area (CPUs-GPUs, distributed nodes). This kind of implementation paradigm allows to design high performing linear algebra algorithms on very different type of architecture: laptop, many-core nodes, CPUs-GPUs, multiple nodes. For example, Chameleon is able to perform a Cholesky factorization (double-precision) at 80 TFlop/s on a dense matrix of order 400 000 (i.e. 4 min 30 s).
• Release Contributions:

  Chameleon includes the following features:

  - BLAS 3, LAPACK one-sided and LAPACK norms tile algorithms - Support QUARK and StarPU runtime systems and PaRSEC since 2018 - Exploitation of homogeneous and heterogeneous platforms through the use of BLAS/LAPACK CPU kernels and cuBLAS/MAGMA CUDA kernels - Exploitation of clusters of interconnected nodes with distributed memory (using OpenMPI)

• URL:
  https://­gitlab.­inria.­fr/­solverstack/­chameleon
• Contact:
  Emmanuel Agullo
• Participants:
  Cédric Castagnede, Samuel Thibault, Emmanuel Agullo, Florent Pruvost, Mathieu Faverge
• Partners:
  Innovative Computing Laboratory (ICL), King Abdullha University of Science and Technology, University of Colorado Denver

6.1.3 Diodon

• Name:
  Diodon
• Keywords:
  Dimensionality reduction, Data analysis
• Functional Description:
  Most of dimension reduction methods inherited from Multivariate Data Analysis, and currently implemented as element in statistical learning for handling very large datasets (the dimension of spaces is the number of features) rely on a chain of pretreatments, a core with a SVD for low rank approximation of a given matrix, and a post-treatment for interpreting results. The costly part in computations is the SVD, which is in cubic complexity. Diodon is a list of functions and drivers which implement (i) pre-treatments, SVD and post-treatments on a large diversity of methods, (ii) random projection methods for running the SVD which permits to bypass the time limit in computing the SVD, and (iii) an implementation in C++ of the SVD with random projection at prescribed rank or precision, connected to MDS.
• URL:
  https://­gitlab.­inria.­fr/­afranc/­diodon
• Authors:
  Alain Franc, Florent Pruvost, Romain Peressoni, Romain Peressoni
• Contact:
  Alain Franc

6.1.4 DPLASMA

• Name:
  Distributed Parallel Linear Algebra Software for Multicore Architectures
• Keywords:
  Dense linear algebra, Linear algebra
• Functional Description:
  DPLASMA is the leading implementation of a dense linear algebra package for distributed heterogeneous systems. It is designed to deliver sustained performance for distributed systems where each node featuring multiple sockets of multicore processors, and if available, accelerators like GPUs or Intel Xeon Phi. DPLASMA achieves this objective through the state of the art PaRSEC runtime, porting the PLASMA algorithms to the distributed memory realm.
• URL:
  http://­icl.­cs.­utk.­edu/­parsec/­index.­html
• Author:
  Mathieu Faverge
• Contact:
  Mathieu Faverge

6.1.5 Fabulous

• Name:
  Fast Accurate Block Linear krylOv Solver
• Keywords:
  Numerical algorithm, Block Krylov solver
• Scientific Description:
  Versatile and flexible numerical library that implements Block Krylov iterative schemes for the solution of linear systems of equations with multiple right-hand sides
• Functional Description:
  Versatile and flexible numerical library that implements Block Krylov iterative schemes for the solution of linear systems of equations with multiple right-hand sides. The library implements block variants of minimal norm residual variants with partial convergence management and spectral information recycling. The package already implements regular block-GMRES (BGMRES), Inexact Breakdown BGMRES (IB-BMGRES), Inexact Breakdown BGMRES with Deflated Restarting (IB-BGMRES-DR), Block Generalized Conjugate Residual with partial convergence management and Inexact Breakdown Block Generalized Conjugate Residual with inner Orthogonalisation and Deflated Restarting (IB-BGCRO-DR). The C++ library relies on callback mechanisms to implement the calculations (matrix-vector, dot-product, ...) that depend on the parallel data distribution selected by the user.
• Release Contributions:
  Added the IB-BGCRO-DR algorithm
• URL:
  https://­gitlab.­inria.­fr/­solverstack/­fabulous/
• Publication:
  hal-01067159
• Contact:
  Luc Giraud
• Participants:
  Emmanuel Agullo, Luc Giraud, Gilles Marait, Cyrille Piacibello, Matthieu Simonin

6.1.6 MAPHYS

• Name:
  Massively Parallel Hybrid Solver
• Keyword:
  Parallel hybrid direct/iterative solution of large linear systems
• Functional Description:

  MaPHyS is a software package that implements a parallel linear solver coupling direct and iterative approaches. The underlying idea is to apply to general unstructured linear systems domain decomposition ideas developed for the solution of linear systems arising from PDEs. The interface problem, associated with the so called Schur complement system, is solved using a block preconditioner with overlap between the blocks that is referred to as Algebraic Additive Schwarz. A fully algebraic coarse space is available for symmetric positive definite problems, that insures the numerical scalability of the preconditioner.

  The parallel implementation is based on MPI+thread. Maphys relies on state-of-the art sparse and dense direct solvers.

  MaPHyS is essentially a preconditioner that can be used to speed-up the convergence of any Krylov subspace method and is coupled with the ones implemented in the Fabulous package.

• URL:
  https://­gitlab.­inria.­fr/­solverstack/­maphys
• Publications:
  hal-01379227, hal-01399203
• Contact:
  Emmanuel Agullo
• Participants:
  Emmanuel Agullo, Luc Giraud, Matthieu Kuhn, Gilles Marait, Louis Poirel

6.1.7 MAPHYS++

• Name:
  Massively Parallel Hybrid Solver in modern C++
• Keywords:
  Linear Systems Solver, Parallel computing, C++, Parallel numerical solvers, Sparse Matrices, Hybrid direct iterative method
• Scientific Description:
  Maphys++ is a parallel linear solver for the resolution of large hollow linear systems that attempts to best combine the advantages of direct methods in terms of robustness and iterative methods in terms of memory footprint and adapted precision. It implements a modern C++ interface (C++17/20), giving the user a wide range of solving methods : efficient direct solver (wrapping MUMPS, Pastix...), iterative solver (CG, GMRES...) and also allowing for a combination of those (hybrid solve using the Schur complement, with adapted preconditioners). Parallelism is based on domain decomposition methods and is implemented in MPI.
• Functional Description:
  MAPHYS++ is a numerical library for solving large sparse linear systems arising from modeling complex phenomena. The library is designed to be used on parallel computers and allows to control the expected accuracy. In a more technical way, the library has a modern C++ interface (C++17/20), allowing a large composability in the solution methods: efficient direct solvers (wrappers to MUMPS, Pastix, ...), iterative solvers (CG, GMRES, ...), as well as the possibility of combining these (hybrid solving using the Schur complement or directly the initial matrix, associated with various preconditioners allowing to control the condition number and consequently the convergence rate in the symmetric positive definite case). The parallelism exploits the domain decomposition principle and implemented in MPI.
• News of the Year:
  The redesign of the package has been completed New release : 1.0 End of 1st development cycle.
• URL:
  https://­gitlab.­inria.­fr/­solverstack/­maphys/­maphyspp
• Contact:
  Emmanuel Agullo
• Participants:
  Emmanuel Agullo, Luc Giraud, Gilles Marait, Matthieu Simonin, Louis Poirel

6.1.8 StarPart

• Keywords:
  High performance computing, HPC, Parallel computing, Graph algorithmics, Graph, Hypergraph
• Functional Description:
  StarPart is a flexible and extensible framework that integrates state-of-the-art methods for graph partitioning and sparse matrix ordering. More precisely, StarPart is a framework that offers a uniform API to manipulate graph, hypergraph and mesh structures. It is designed to be easily extensible by adding new methods and to plug all these methods into a comprehensive framework. It is initially designed to provide graph partitioning and sparse matrix ordering methods, that come from sate-of-the-art software such as Metis, Scotch, Patoh, Zoltan, etc. Besides, it provides some facilities for IO, diagnostic, benchmark, visualization (VTK, SVG, ...). StarPart is the core of the MetaPart project. It is built upon the LibGraph library.
• URL:
  https://­gitlab.­inria.­fr/­metapart/­starpart
• Contact:
  Aurélien Esnard
• Participant:
  Aurélien Esnard

6.1.9 MPICPL

• Name:
  MPI CouPLing
• Keywords:
  MPI, Coupling software
• Functional Description:
  MPICPL is a software library dedicated to the coupling of parallel legacy codes, that are based on the well-known MPI standard. It proposes a lightweight and comprehensive programing interface that simplifies the coupling of several MPI codes (2, 3 or more). MPICPL facilitates the deployment of these codes thanks to the mpicplrun tool and it interconnects them automatically through standard MPI inter-communicators. Moreover, it generates the universe communicator, that merges the world communicators of all coupled-codes. The coupling infrastructure is described by a simple XML file, that is just loaded by the mpicplrun tool.
• URL:
  https://­gitlab.­inria.­fr/­esnard/­mpicpl
• Contact:
  Aurélien Esnard
• Participant:
  Aurélien Esnard

6.1.10 OptiDis

• Keywords:
  Dislocation dynamics simulation, Fast multipole method, Large scale, Collision
• Functional Description:
  OptiDis is a new code for large scale dislocation dynamics simulations. Its purpose is to simulate real life dislocation densities (up to 5.1022 dislocations/m-2) in order to understand plastic deformation and study strain hardening. The main application is to observe and understand plastic deformation of irradiated zirconium. Zirconium alloys are the first containment barrier against the dissemination of radioactive elements. More precisely, with neutron irradiated zirconium alloys we are talking about channeling mechanism, which means to stick with the reality, more than tens of thousands of induced loops, i. e. 100 million degrees of freedom in the simulation. The code is based on Numodis code developed at CEA Saclay and the ScalFMM library developed in HiePACS project. The code is written in C++ language and using the last features of C++11/14. One of the main aspects is the hybrid parallelism MPI/OpenMP that gives the software the ability to scale on large cluster while the computation load rises. In order to achieve that, we use different levels of parallelism. First of all, the simulation box is distributed over MPI processes, then we use a thinner level for threads, dividing the domain by an Octree representation. All theses parts are controlled by the ScalFMM library. On the last level, our data are stored in an adaptive structure that absorbs the dynamics of this type of simulation and manages the parallelism of tasks..
• URL:
  https://­gitlab.­inria.­fr/­optidis/­optidis
• Publication:
  hal-01086371
• Contact:
  Olivier Coulaud
• Participant:
  Olivier Coulaud
• Partner:
  CEA

6.1.11 PaStiX

• Name:
  Parallel Sparse matriX package
• Keywords:
  Linear algebra, High-performance calculation, Sparse Matrices, Linear Systems Solver, Low-Rank compression
• Scientific Description:
  PaStiX is based on an efficient static scheduling and memory manager, in order to solve 3D problems with more than 50 million of unknowns. The mapping and scheduling algorithm handles a combination of 1D and 2D block distributions. A dynamic scheduling can also be applied to take care of NUMA architectures while taking into account very precisely the computational costs of the BLAS 3 primitives, the communication costs and the cost of local aggregations.
• Functional Description:

  PaStiX is a scientific library that provides a high performance parallel solver for very large sparse linear systems based on block direct and block ILU(k) methods. It can handle low-rank compression techniques to reduce the computation and the memory complexity. Numerical algorithms are implemented in single or double precision (real or complex) for LLt, LDLt and LU factorization with static pivoting (for non symmetric matrices having a symmetric pattern). The PaStiX library uses the graph partitioning and sparse matrix block ordering packages Scotch or Metis.

  The PaStiX solver is suitable for any heterogeneous parallel/distributed architecture when its performance is predictable, such as clusters of multicore nodes with GPU accelerators or KNL processors. In particular, we provide a high-performance version with a low memory overhead for multicore node architectures, which fully exploits the advantage of shared memory by using a hybrid MPI-thread implementation.

  The solver also provides some low-rank compression methods to reduce the memory footprint and/or the time-to-solution.

• URL:
  https://­gitlab.­inria.­fr/­solverstack/­pastix
• Contact:
  Pierre Ramet
• Participants:
  Tony Delarue, Grégoire Pichon, Mathieu Faverge, Esragul Korkmaz, Pierre Ramet
• Partners:
  INP Bordeaux, Université de Bordeaux

6.1.12 pmtool

• Keywords:
  Scheduling, Task scheduling, StarPU, Heterogeneity, GPGPU, Performance analysis
• Functional Description:
  Analyse post-mortem the behavior of StarPU applications. Provide lower bounds on makespan. Study the performance of different schedulers in a simple context. Provide implementations of many scheduling algorithms from the literature
• News of the Year:
  Included many new algorithms, in particular online algorithms Better integration with StarPU by accepting .rec files as input
• URL:
  https://­gitlab.­inria.­fr/­eyrauddu/­pmtool
• Publications:
  hal-01386174, hal-01878606
• Contact:
  Lionel Eyraud Dubois
• Participant:
  Lionel Eyraud Dubois

6.1.13 rotor

• Name:
  Re-materializing Optimally with pyTORch
• Keywords:
  Deep learning, Optimization, Python, GPU, Automatic differentiation
• Scientific Description:

  This software implements in PyTorch a new activation checkpointing method which allows to significantly decrease memory usage when training Deep Neural Networks with the back-propagation algorithm. Similarly to checkpointing techniques coming from the literature on Automatic Differentiation, it consists in dynamically selecting the forward activations that are saved during the training phase, and then automatically recomputing missing activations from those previously recorded. We propose an original computation model that combines two types of activation savings: either only storing the layer inputs, or recording the complete history of operations that produced the outputs (this uses more memory, but requires fewer recomputations in the backward phase), and we provide in https://hal.inria.fr/hal-02352969 an algorithm to compute the optimal computation sequence for this model.

  Our PyTorch implementation processes the entire chain, dealing with any sequential DNN whose internal layers may be arbitrarily complex and automatically executing it according to the optimal checkpointing strategy computed given a memory limit. In https://hal.inria.fr/hal-02352969, through extensive experiments, we show that our implementation consistently outperforms existing checkpoint-ing approaches for a large class of networks, image sizes and batch sizes.

• Functional Description:
  Allows to train very large convolutional networks on limited memory by optimally selecting which activations should be kept and which should be recomputed. This code is meant to replace the checkpoint.py utility available in pytorch, by providing more efficient rematerialization strategies. The algorithm is easier to tune: the only required parameter is the available memory, instead of the number of segments.
• URL:
  https://­gitlab.­inria.­fr/­hiepacs/­rotor
• Publication:
  hal-02352969
• Contact:
  Lionel Eyraud Dubois
• Participants:
  Olivier Beaumont, Alena Shilova, Alexis Joly, Lionel Eyraud Dubois, Julien Herrmann

6.1.14 ScalFMM

• Name:
  Scalable Fast Multipole Method
• Keywords:
  N-body, Fast multipole method, Parallelism, MPI, OpenMP
• Scientific Description:

  ScalFMM is a software library to simulate N-body interactions using the Fast Multipole Method. The library offers two methods to compute interactions between bodies when the potential decays like 1/r. The first method is the classical FMM based on spherical harmonic expansions and the second is the Black-Box method which is an independent kernel formulation (introduced by E. Darve @ Stanford). With this method, we can now easily add new non oscillatory kernels in our library. For the classical method, two approaches are used to decrease the complexity of the operators. We consider either matrix formulation that allows us to use BLAS routines or rotation matrix to speed up the M2L operator.

  ScalFMM intends to offer all the functionalities needed to perform large parallel simulations while enabling an easy customization of the simulation components: kernels, particles and cells. It works in parallel in a shared/distributed memory model using OpenMP and MPI. The software architecture has been designed with two major objectives: being easy to maintain and easy to understand. There is two main parts:

  the management of the octree and the parallelization of the method the kernels. This new architecture allow us to easily add new FMM algorithm or kernels and new paradigm of parallelization.

• Functional Description:
  Compute N-body interactions using the Fast Multipole Method for large number of objects
• URL:
  https://­gitlab.­inria.­fr/­solverstack/­ScalFMM
• Contact:
  Olivier Coulaud
• Participants:
  Bramas Bérenger, Olivier Coulaud, Pierre Estérie

6.1.15 VITE

• Name:
  Visual Trace Explorer
• Keywords:
  Visualization, Execution trace
• Functional Description:
  ViTE is a trace explorer. It is a tool made to visualize execution traces of large parallel programs. It supports Pajé, a trace format created by Inria Grenoble, and OTF and OTF2 formats, developed by the University of Dresden and allows the programmer a simpler way to analyse, debug and/or profile large parallel applications.
• URL:
  https://­solverstack.­gitlabpages.­inria.­fr/­vite/
• Contact:
  Mathieu Faverge
• Participant:
  Mathieu Faverge

6.1.16 PlaFRIM

• Name:
  Plateforme Fédérative pour la Recherche en Informatique et Mathématiques
• Keywords:
  High-Performance Computing, Hardware platform
• Functional Description:

  PlaFRIM is an experimental platform for research in modeling, simulations and high performance computing. This platform has been set up from 2009 under the leadership of Inria Bordeaux Sud-Ouest in collaboration with computer science and mathematics laboratories, respectively Labri and IMB with a strong support in the region Aquitaine.

  It aggregates different kinds of computational resources for research and development purposes. The latest technologies in terms of processors, memories and architecture are added when they are available on the market. It is now more than 1,000 cores (excluding GPU and Xeon Phi ) that are available for all research teams of Inria Bordeaux, Labri and IMB. This computer is in particular used by all the engineers who work in HiePACS and are advised by F. Rue from the SED.

• URL:
  https://­www.­plafrim.­fr/­en/­home/
• Contact:
  Olivier Coulaud

7.1.1 Resiliency in numerical algorithm design for extreme scale simulations

This work is based on the seminar titled “Resiliency in Numerical Algorithm Design for Extreme Scale Simulations” held March 1-6, 2020 at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 hours on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 1023 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications, and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.

For more information on this work we refer to  15.

7.1.2 Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Progress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys hardware, application-level and algorithm-level resilience approaches of particular relevance to timecritical numerical weather and climate prediction systems. A selection of applicable existing strategies is analysed, featuring interpolation-restart and compressed checkpointing for the numerical schemes, in-memory checkpointing, user-level failure mitigation and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analysed and some recommendations outlined for future developments.

For more information on this work we refer to 16.

7.1.3 TEXTAROSSA: Towards EXtreme scale Technologies and Accelerators for euROhpc hw/Sw Supercomputing Applications for exascale

To achieve high performance and high energy efficiency on near-future exascale computing systems, three key technology gaps needs to be bridged. These gaps include: energy efficiency and thermal control; extreme computation efficiency via HW acceleration and new arithmetics; methods and tools for seamless integration of reconfigurable accelerators in heterogeneous HPC multi-node platforms. TEXTAROSSA aims at tackling this gap through a co-design approach to heterogeneous HPC solutions, supported by the integration and extension of HW and SW IPs, programming models and tools derived from European research.

More information on this project can be found in 21.

7.2.1 Comparison of coupled solvers for FEM/BEM linear systems arising from discretization of aeroacoustic problems

When discretization of an aeroacoustic physical model is based on the application of both the Finite Elements Method (FEM) and the Boundary Elements Method (BEM), this leads to coupled FEM/BEM linear systems combining sparse and dense parts. In this work, we propose and compare a set of implementation schemes relying on the coupling of the open-source sparse direct solver MUMPS with the proprietary direct solvers from Airbus Central R&T, i.e. the scalapack-like dense solver SPIDO and the hierarchical $\mathscr{H}$-matrix compressed solver HMAT. For this preliminary study, we limit ourselves to a single 24-core computational node.

For more information on this work we refer to 26 and 28.

7.2.2 Recycling Krylov subspace strategies for sequences of sampled stochastic elliptic equations

We are interested in the quantification of uncertainties in discretized elliptic partial differential equations with a random coefficient field. In sampling-based approaches, this relies on solving large numbers of symmetric positive definite (SPD) linear systems with different matrices. In particular, we consider the case in which these operators are sampled by Markov chain Monte Carlo, which leads to sequences of correlated matrices. We investigate recycling Krylov subspace strategies for the iterative solution of sequences of linear systems formed with such matrices. The linear systems are solved using initialized conjugate gradient (Init-CG) methods, where approximate eigenvectors of the previously sampled operator are used to set an initial guess, and deflated conjugate gradient (Def-CG) methods, where the Krylov subspace is augmented with these vectors. The following aspects of eigenvector approximation, and their effect on deflation and initialization, are investigated in this context: (i) projection technique, and (ii) refreshing strategy of the eigen-search space. Our numerical experiments show that, when not using a preconditioner, these aspects only impact convergence behaviors of Def-CG at the early stages of the sampling sequence. Second, unlike sequences with multiple right-hand sides and a constant operator, our experiments with multiple matrices show that, even for highly correlated matrices, Init-CG does not reproduce the convergence behavior of Def-CG. Finally, the limits of deflation used as a means to compensate for the inefficiency of block-Jacobi (bJ) preconditioners are investigated. For small systems, using a bJ preconditioner while deflating with at least as many approximate eigenvectors as the number of bJ blocks achieves similar convergence behaviors to PCG with a constant algebraic multigrid (AMG) preconditioner. For larger systems, although the effect of deflation is improved when using the right refreshing strategy of the eigen-search space, the combination of deflation with bJ preconditioners does not scale as well as using PCG with a constant AMG preconditioner based on the median realization of the coefficient field.

For more information on this work we refer to 33.

7.2.3 A block minimum residual norm subspace solver with partial convergence management for sequences of linear systems

We are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another, including the case where there are massive number (like tens of thousands) of right-hand sides associated with a single matrix so that all of them cannot be solved at once but rather need to be split into chunks of possible variable sizes. For such sequences of linear systems with multiple left and right-hand sides, we develop a new recycling block generalized conjugate residual method with inner orthogonalization and inexact breakdown (IB-BGCRO-DR), which glues subspace recycling technique in GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651–1674] and inexact breakdown mechanism in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265–285] to guarantee this new algorithm could reuse spectral information for subsequent cycles as well as for the remaining linear systems to be solved. Related variant IB-BFGCRO-DR that suits for flexible preconditioning is devised to cope with constraints on some applications while also enabling mixed-precision calculation, which provides advantages in speed and memory usage over double precision as well as in perspective of emerging computing units such as the GPUs.

For more information on this work we refer to 31 that is a preliminary version of a paper recently accepted in SIMAX.

7.2.4 Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization

Low-rank compression techniques are very promising for reducing memory footprint and execution time on a large spectrum of linear solvers. Sparse direct supernodal approaches are one of these techniques. However, despite providing a very good scalability and reducing the memory footprint, they suffer from an important flops overhead in their unstructured low-rank updates. As a consequence, the execution time is not improved as expected. In this paper, we study a solution to improve low-rank compression techniques in sparse supernodal solvers. The proposed method tackles the overprice of the low-rank updates by identifying the blocks that have poor compression rates. We show that the fill-in levels of the graph based block incomplete LU factorization can be used in a new context to identify most of these non-compressible blocks at low cost. This identification enables to postpone the low-rank compression step to trade small extra memory consumption for a better time to solution. The solution is validated within the PaStiX library with a large set of application matrices. It demonstrates sequential and multithreaded speedup up to 8.5×, for small memory overhead of less than 1.49× with respect to the original version.

For more information on this work we refer to 25.

7.3.1 Solving eigenvalue problems using contour integration in Tensor Train format

In high-dimension, solving an eigenvalue problem encounters several issues related to the curse of dimensionality especially when only eigenvalues in a given interval are desired. To overcome these difficulties, we consider the FEAST algorithm that is developed for solving a Hermitian eigenproblem inside a given interval and based on a contour integration that projects the matrix pencil onto the subspace associated with the eigenpairs is the desired interval. We also consider the tensor-train decomposition (TT) for the operators and the eigenvectors to overcome the curse of dimensionality and reduce the required storage. In this paper, we extend the FEAST algorithm to match with the TT representation of operators and vectors to form an algorithm that computes the eigenvalue problems in an interval based on operations in TT-format. The proposed algorithm is applied on some high-dimensional problems, including the Laplacian operator and the vibrational Hamiltonian, and it shows a high efficiency and accuracy. We validate the results by comparing with an analytical solution for Laplacian operator, and with an existing method in TT-format for computing certain minimal eigenpairs.

The scientific report describing this work should be published in early 2022.

7.3.2 Iterative linear solver in tensorial spaces

In this work, we studied the solution of linear systems defined in tensor spaces of different dimensions. Specifically, we considered nested subspace techniques in tensor format for the solution of 3d (PDEs in a 3-dimensional space), 4d (parametric PDEs, or 3D PDEs with multiple right-hand sides), 5d (time-dependent parametric PDEs) linear problems. In particular, we have derived bounds to evaluate the quality of the solutions computed in low-rank tensor format compared to their more classical linear algebra counterparts.

The scientific report describing this work should be published in early 2022.

7.4.1 High Order Singular Value Decomposition for Plant Biodiversity Estimation

We propose a new method to estimate plant biodiversity with Rényi and Rao indexes through the so called High Order Singular Value Decomposition (HOSVD) of tensors. Starting from NASA multispectral images we evaluate biodiversity and we compare original biodiversity estimates with those realised via the HOSVD compression methods for big data. Our strategy turns out to be extremely powerful in terms of storage memory and precision of the outcome. The obtained results are so promising that we can support the efficiency of our method in the ecological framework.

For more information on this work we refer to 17.

7.4.2 Correspondence Analysis to multiway data-sets through High Order SVD

In this work we propose an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component analysis, for studying contingency tables. Different algebraic extensions of CA to multi-way tables have been proposed over the years, nevertheless neglecting its geometric meaning. Relying on the Tucker model and the HOSVD, we propose a direct way to associate with each tensor mode a point cloud. We prove that the point clouds are related to each other. Specifically using the CA metrics we show that the barycentric relation is still true in the tensor framework. Finally two data sets are used to underline the advantages and the drawbacks of our strategy with respect to the classical matrix approaches.

For more information on this work we refer to 30.

7.5.1 A note on the strong parallel scalability of numerically scalable Poisson linear solvers

In the context of a parallel plasma physics simulation code, we perform a qualitativeperformance study between two natural candidates for the parallel solution of 3D Poisson problemsthat are multigrid and domain decomposition. We selected one representative of each of thesenumerical techniques implemented in state of the art parallel packages and show that dependingon the regime used in terms of number of unknowns per computing cores the best alternative interms of time to solution varies. Those results show the interest of having both types of numericalsolvers integrated in a simulation code that can be used in very different configurations in termsof selected modelisations, problem sizes and parallel computing platforms.

For more information on this work we refer to  29.

7.5.2 The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code.

For more information on this work we refer to  19.

7.6.1 Pipelined Model Parallelism: Complexity Results and Memory Considerations

The training phase in Deep Neural Networks has become an important source of computing resource usage and the resulting volume of computation makes it crucial to perform efficiently on parallel architectures. Data parallelism is the most widely used method, but it requires to replicate the network weights on all processors, and to perform collective communications of the network weights. In this context, model parallelism is an attractive alternative, in which the different layers of the network are distributed over the computing processors. Indeed, it is expected to better distribute weights (to cope with memory problems) and it eliminates the need for large collective communications since only forward activations are communicated. However, to be efficient, it must be combined with a pipelined approach, which in turn induces new memory costs. We have thus worked to formalize pipelined model parallelism as a scheduling problem, to establish its complexity, and to analyze the consequences of the assumptions that are typically performed in practical solutions such as Pipedream.

More information on this work can be found in 23.

7.6.2 Efficient Combination of Rematerialization and Offloading for Training DNNs

Rematerialization and offloading are two well known strategies to save memory during the training phase of deep neural networks, allowing data scientists to consider larger models, batch sizes or higher resolution data. Rematerialization trades memory for computation time, whereas Offloading trades memory for data movements. As these two resources are independent, it is appealing to consider the simultaneous combination of both strategies to save even more memory. We precisely model the costs and constraints corresponding to Deep Learning frameworks such as PyTorch or Tensorflow, we propose optimal algorithms to find a valid sequence of memory-constrained operations and finally, we evaluate the performance of proposed algorithms on realistic networks and computation platforms. Our experiments show that the possibility to offload can remove one third of the overhead of rematerialization, and that together they can reduce the memory used for activations by a factor 4 to 6, with an overhead below 20

More information on this work can be found in 22.

7.7.1 READYS: A Reinforcement Learning Based Strategy for Heterogeneous Dynamic Scheduling

We have proposed READYS, a reinforcement learning algorithm for the dynamic scheduling of computations modeled as a Directed Acyclic Graph (DAGs). Our goal is to develop a scheduling algorithm in which allocation and scheduling decisions are made at runtime, based on the state of the system, as performed in runtime systems such as StarPU or ParSEC. Reinforcement Learning is a natural candidate to achieve this task, since its general principle is to build step by step a strategy that, given the state of the system (the state of the resources and a view of the ready tasks and their successors in our case), makes a decision to optimize a global criterion. Moreover, the use of Reinforcement Learning is natural in a context where the duration of tasks (and communications) is stochastic. We propose READYS that combines Graph Convolutional Networks (GCN) with an Actor-Critic Algorithm (A2C): it builds an adaptive representation of the scheduling problem on the fly and learns a scheduling strategy, aiming at minimizing the makespan. A crucial point is that READYS builds a general scheduling strategy which is neither limited to only one specific application or task graph nor one particular problem size, and that can be used to schedule any DAG. We focus on different types of task graphs originating from linear algebra factorization kernels (CHOLESKY, LU, QR) and we consider heterogeneous platforms made of a few CPUs and GPUs. We first propose to analyze the performance of READYS when learning is performed on a given (platform, kernel, problem size) combination. Using simulations, we show that the scheduling agent obtains performance very similar or even superior to algorithms from the literature, and that it is especially powerful when the scheduling environment contains a lot of uncertainty. We additionally demonstrate that our agent exhibits very promising generalization capabilities. To the best of our knowledge, this is the first paper which shows that reinforcement learning can really be used for dynamic DAG scheduling on heterogeneous resources.

More information on this work can be found in 24.

9.1.1 Inria associate team not involved in an IIL or an international program

9.2.1 FP7 & H2020 projects

9.3.1 ANR

9.3.2 FUI

9.3.3 Inria Project Labs

10.1.1 Scientific events: organisation

10.1.2 Scientific events: selection

10.1.3 Journal

10.1.4 Scientific expertise

• Olivier Beaumont acted as expert for 2020 FET Open Evaluation Committee.

• Luc Giraud is member of the board on Modelization, Simulation and data analysis of the Competitiveness Cluster for Aeronautics, Space and Embedded Systems. He is also member of the scientific council of the ONERA Lab LMA2S (Laboratoire de Mathématiques Appliquées à l'Aéronautique et au Spatial).

  He also acted as expert for the Czech Science Foundation.

• Pierre Ramet is Scientific Advisor at the CEA-DAM CESTA.
• Guillaume Sylvand is Expert in Numerical Simulation and HPC at Airbus.

10.1.5 Research administration

• P. Ramet is the head of the SATANAS (Supports and Algorithms for High Performance Numerical Applications) team from LaBRI UMR CNRS 5800.

10.2.1 Teaching

• Undergraduate level/Licence:
  • A. Esnard: System programming 36h, Computer architecture 40h, Network 23h, C programming 35h at Bordeaux University. He is also responsible for the second year of the computer science degree (L2 Informatique), which involves managing about 200 students each year.
  • M. Faverge: Programming environment 26h, Numerical algorithmic 40h, C projects 25h at Bordeaux INP (ENSEIRB-MatMeca).
  • A. Guermouche: System programming 36h at Bordeaux University.
  • P. Ramet: System programming 24h, Databases 32h, Object programming 48h, Distributed programming 16h, Cryptography 16h, Introduction to AI Deep Learning and Data Analytics 16h at Bordeaux University.
• Post graduate level/Master:
  • E. Agullo: Operating systems 24h at Bordeaux University ; Dense linear algebra kernels 8h, Numerical algorithms 30h at Bordeaux INP (ENSEIRB-MatMeca).
  • O. Coulaud: Paradigms for parallel computing 8h, Introduction to Tensor methods 4h at Bordeaux INP (ENSEIRB-MatMeca).
  • A. Esnard: Network management 27h, Network security 27h at Bordeaux University; Programming distributed applications 35h at Bordeaux INP (ENSEIRB-MatMeca).
  • L. Eyraud-Dubois and Olivier Beaumont: Approximation and BigData 24h at Bordeaux University.
  • M. Faverge: System programming 72h, Linear Algebra for high Performance Computing 13h at Bordeaux INP (ENSEIRB-MatMeca). He is also in charge of the master 2 internship for the Computer Science department at Bordeaux INP (ENSEIRB-MatMeca). Starting in September, he is in charge with Raymond Namyst of the High Performance Computing - High Performance Data Analytics option at ENSEIRB-MatMeca. This is a common training curriculum between the Computer Science and MatMeca departments at Bordeaux INP and with Bordeaux University in the context of the Computer Science Research Master.
  • Alena Shilova and Olivier Beaumont: Deep Learning Frameworks, at Bordeaux INP (ENSEIRB-MatMeca), 20h.
  • Olivier Beaumont, Sketching and Streaming Algorithms, ENS Lyon, 8h.
  • L. Giraud: Introduction to intensive computing and related programming tools 30h, INSA Toulouse; On mathematical tools for numerical simulations 10h, ENSEEIHT Toulouse.
  • A. Guermouche: Network management 92h, Network security 64h, Operating system 24h at Bordeaux University.
  • P. Ramet: Cryptography 20h and Numerical algorithms 40h at Bordeaux INP (ENSEIRB-Matmeca).
• High School teachers:
  • A. Esnard, M. Faverge, and A. Guermouche participated to the training of the High School teachers (DIU Enseigner l'Informatique au Lycée) in computer science for the new computer science program starting in September 2019.

10.2.2 Supervision

• PhD in progress: Tobias Castanet; Replication algorithms for multi-player virtual worlds; started Sep. 2019; O. Beaumont, N. Hanusse (LaBRI), C. Travers (Bordeaux INP - LaBRI).
• PhD in progress: Marek Felsoci; Fast solvers for high-frequency aeroacoustics; started Oct. 2019; G. Sylvand, E. Agullo.
• PhD in progress: Martina Iannacito; Linear solvers in tensorial format for high dimensional problems; started Oct 2019; O. Coulaud, L. Giraud.
• PhD in progress: Esragul Korkmaz; Sparse linear solver and hierachical matrices; started Nov. 2018; M. Faverge, P. Ramet.
• PhD in progress: Romain Peressoni; Fast multidimensional scaling method for the study of biodiversity; started Oct 2019; E. Agullo, O. Coulaud, A. Franc (PLEIADE).
• PhD in progress: Aboul-Karim Mohamed El Maarouf; Parallel fine grain imcomplete LU factorization for the solution of sparse linear systems; started: Dec. 2019; L. Giraud, A. Guermouche.
• PhD in progress: Clément Richefort; Multigrid methods applied to electromagnetism problems; started Nov. 2021; P. Ramet, M. Lecouvez (CEA Cesta).
• PhD in progress: Alena Shilova; Scheduling for deep learning applications; started Oct. 2018; L. Eyraud-Dubois, O. Beaumont.
• PhD in progress: Nicolas Venkovic; Domain decomposition techniques for the solution of stochastics elliptic PDEs; started Nov. 2018; L. Giraud, P. Mycek (Cerfacs).
• PhD in progress: Mathieu Vérité; Static allocation algorithms for scheduling High-Performance applications; started Sept. 2019; L. Eyraud-Dubois, O. Beaumont.
• PhD in progress: Yanfei Xiang; Solution of large linear systems with massive numbers of right-hand sides. Started Nov. 2019; L. Giraud, P. Mycek (Cerfacs).

10.2.3 Juries

• Ashish Bhole, "Stabilized C1-bicubic finite element method for nonlinear MHD modelling of tokamak plasma"; referees: Eric Serre, Eric Nardon; members: Dinshaw Balsara, Hervé Guillard, Boniface Nkonga, Stanislas Pamela, Pierre Ramet; Université Cote d'Azur, 17 Nov. 2021.
• J. F. Reis, “Preconditioning of domain decomposition methods for stochastic elliptic equations"; referees: Anthony Nouy, Luc Giraud; members: frédéric Hecht, Nicole Spillane, Paul Mycek, Pietro Congedo, Olivier Le Maitre; Institut Polytechnique de Paris - Ecole polytechnique, Spécialité: mathématiques appliquées; 4 Oct. 2021.
• K.E. Prikopa, "Fault tolerant linear least squares solvers and matrix multiplication in parallel and distributed environments"; referees: Jesper Larson Traff, Luc Giraud; members: Helmut Hlavacs, Wielfrid Gansterer; University of Vienna; 14 Oct. 2021.

10.3.1 Internal or external Inria responsibilities

Pierre Ramet is member of the CDT (Technological Development Commission) at inria Bordeaux since 2015.

International journals

• 15 articleE.Emmanuel Agullo, M.Mirco Altenbernd, H.Hartwig Anzt, L.Leonardo Bautista-Gomez, T.Tommaso Benacchio, L.Luca Bonaventura, H.-J.Hans-Joachim Bungartz, S.Sanjay Chatterjee, F. M.Florina M Ciorba, N.Nathan Debardeleben, D.Daniel Drzisga, S.Sebastian Eibl, C.Christian Engelmann, W. N.Wilfried N Gansterer, L.Luc Giraud, D.Dominik Göddeke, M.Marco Heisig, F.Fabienne Jézéquel, N.Nils Kohl, S.Sherry Xiaoye, R.Romain Lion, M.Miriam Mehl, P.Paul Mycek, M.Michael Obersteiner, E. S.Enrique S Quintana-Ortí, F.Francesco Rizzi, U.Ulrich Rüde, M.Martin Schulz, F.Fred Fung, R.Robert Speck, L.Linda Stals, K.Keita Teranishi, S.Samuel Thibault, D.Dominik Thönnes, A.Andreas Wagner and B.Barbara Wohlmuth. Resiliency in numerical algorithm design for extreme scale simulations.International Journal of High Performance Computing ApplicationsSeptember 2021
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• 16 articleT.Tommaso Benacchio, L.Luca Bonaventura, M.Mirco Altenbernd, C. D.Chris D Cantwell, P. D.Peter D Düben, M.Mike Gillard, L.Luc Giraud, D.Dominik Göddeke, E.Erwan Raffin, K.Keita Teranishi and N.Nils Wedi. Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction.International Journal of High Performance Computing Applications354February 2021, 285-311
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• 17 articleA.Alessandra Bernardi, M.Martina Iannacito and D.Duccio Rocchini. High Order Singular Value Decomposition for Plant Biodiversity Estimation.Bollettino dell'Unione Matematica ItalianaJune 2021
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• 18 articleL.Luc Giraud, Y.-F.Y.-F Jing and Y.-F.Y.-F Xiang. A block minimum residual norm subspace solver with partial convergence management for sequences of linear systems.SIAM Journal on Matrix Analysis and Applications2022
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• 19 articleM.Matthias Hoelzl, G.Guido Huijsmans, S.Stanislas Pamela, M.Marina Bécoulet, E.Eric Nardon, F. J.Francisco Javier Artola, B.Boniface Nkonga, C. V.Calin Vlad Atanasiu, V.Vinodh Bandaru, A.Ashish Bhole, D.Daniele Bonfiglio, A.Andres Cathey, O.Olivier Czarny, A.Anastasia Dvornova, T.Tamas Fehér, A.Alexandre Fil, E.Emmanuel Franck, S.Shimpei Futatani, M.Marta Gruca, H.Hervé Guillard, W. J.Willem J. Haverkort, I.Ihor Holod, D.Di Hu, S.S.K. Kim, S. Q.Sven Q. Korving, L.Leon Kos, I.Isabel Krebs, L.Lukas Kripner, G.Guillaume Latu, F.Franklin Liu, P.Peter Merkel, D.Dmytro Meshcheriakov, V.Verena Mitterauer, S.Serhiy Mochalskyy, J. A.Jorge A. Morales, R.Richard Nies, N.Nikita Nikulsin, F.François Orain, J.Jane Pratt, R.Rohan Ramasamy, P.Pierre Ramet, C.Cédric Reux, K.Konsta Särkimäki, N.N. Schwarz, P. S.Prabal Singh Verma, S.Siobhan Smith F., C.Cristian Sommariva, E.Erika Strumberger, D. C.Daan C. van Vugt, M.M. Verbeek, E.Egbert Westerhof, F.Fabian Wieschollek and J.Jeffery Zielinski. The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas.Nuclear Fusion616May 2021, 065001
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• 20 articleD.Duccio Rocchini, E.Elisa Thouverai, M.Matteo Marcantonio, M.Martina Iannacito, D.Daniele Da Re, M.Michele Torresani, G.Giovanni Bacaro, M.Manuele Bazzichetto, A.Alessandra Bernardi, G. M.Giles M. Foody, R.Reinhard Furrer, D.David Kleijn, S.Stefano Larsen, J. R.Jonathan Roger Michel Henri Lenoir, M.Marco Malavasi, E.Elisa Marchetto, F.Filippo Messori, A.Alessandro Montaghi, V.Vitezslav Moudry, B.Babak Naimi, C.Carlo Ricotta, M.Micol Rossini, F.Francesco Santi, M. J.Maria J. Santos, M. E.Michael E. Schaepman, F. D.Fabian D. Schneider, L.Leila Schuh, S.Sonia Silvestri, P.Petra Simova, A. K.Andrew K. Skidmore, C.Clara Tattoni, E.Enrico Tordoni, S.Saverio Vicario, P.Piero Zannini and M.Martin Wegmann. rasterdiv-An Information Theory tailored R package for measuring ecosystem heterogeneity from space: To the origin and back.Methods in Ecology and Evolution1262021, 1093-1102
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International peer-reviewed conferences

• 21 inproceedingsG.Giovanni Agosta, D.Daniele Cattaneo, W.William Fornaciari, A.Andrea Galimberti, G.Giuseppe Massari, F.Federico Reghenzani, F.Federico Terraneo, D.Davide Zoni, C.Carlo Brandolese, M.Massimo Celino, F.Francesco Iannone, P.Paolo Palazzari, G.Giuseppe Zummo, M.Massimo Bernaschi, P.Pasqua D'Ambra, S.Sergio Saporana, M.Marco Danelutto, M.Massimo Torquati, M.Marco Aldinucci, Y.Yasir Arfat, B.Barbara Cantalupo, I.Iacopo Colonnelli, R.Roberto Esposito, A. R.Alberto Riccardo Martinelli, G.Gianluca Mittone, O.Olivier Beaumont, B.Bérenger Bramas, L.Lionel Eyraud-Dubois, B.Brice Goglin, A.Abdou Guermouche, R.Raymond Namyst, S.Samuel Thibault, A.Antonio Filgueras, M.Miquel Vidal, C.Carlos Alvarez, X.Xavier Martorell, A.Ariel Oleksiak, O.Ottorino Frezza, M.Michal Kulczewski, A.Alessandro Lonardo, P.Piero Vicini, F.Francesca Lo Cicero, F.Francesca Simula, A.Andrea Biagioni, P.Paolo Cretaro, P.Pier Stanislao Paolucci, M.Matteo Turisini, F.Francesco Giacomini, T.Tommaso Boccali, S.Simone Montangero and R.Roberto Ammendola. TEXTAROSSA: Towards EXtreme scale Technologies and Accelerators for euROhpc hw/Sw Supercomputing Applications for exascale.DSD 2021 - 24th Euromicro Conference on Digital System DesignPalermo / Virtual, ItalySeptember 2021
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• 22 inproceedingsO.Olivier Beaumont, L.Lionel Eyraud-Dubois and A.Alena Shilova. Efficient Combination of Rematerialization and Offloading for Training DNNs.NeurIPS 2021 - Thirty-fifth Conference on Neural Information Processing SystemsVirtual-only Conference, FranceDecember 2021
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• 23 inproceedingsO.Olivier Beaumont, L.Lionel Eyraud-Dubois and A.Alena Shilova. Pipelined Model Parallelism: Complexity Results and Memory Considerations.Europar 2021Proceedings of Europar 2021Lisbon, PortugalSpringer2021
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• 24 inproceedingsN.Nathan Grinsztajn, O.Olivier Beaumont, E.Emmanuel Jeannot and P.Philippe Preux. READYS: A Reinforcement Learning Based Strategy for Heterogeneous Dynamic Scheduling.IEEE Cluster 2021Portland / Virtual, United StatesSeptember 2021
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• 25 inproceedingsE.Esragul Korkmaz, M.Mathieu Faverge, G.Grégoire Pichon and P.Pierre Ramet. Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization.HiPC 2021 - 28th IEEE International Conference on High Performance Computing, Data, and AnalyticsBangalore, IndiaIEEEDecember 2021, 1-10
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Conferences without proceedings

• 26 inproceedingsE.Emmanuel Agullo, M.Marek Felšöci and G.Guillaume Sylvand. Comparison of coupled solvers for FEM/BEM linear systems arising from discretization of aeroacoustic problems.COMPAS 2021 - Conférence francophone d'informatique en Parallélisme, Architecture et SystèmeLyon / Virtuel, FranceInria Bordeaux Sud-OuestJune 2021
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Reports & preprints

• 27 reportE.Emmanuel Agullo, M.Marek Felšöci and G.Guillaume Sylvand. A comparison of selected solvers for coupled FEM/BEM linear systems arising from discretization of aeroacoustic problems.RR-9412Inria Bordeaux Sud-OuestJune 2021, 52
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• 28 reportE.Emmanuel Agullo, M.Marek Felšöci and G.Guillaume Sylvand. A comparison of selected solvers for coupled FEM/BEM linear systems arising from discretization of aeroacoustic problems: literate and reproducible environment.RT-0513Inria Bordeaux Sud-OuestJune 2021, 100
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• 29 reportE.Emmanuel Agullo, L.Luc Giraud, V.Valentin Joncquieres, G.Gilles Marait, L.Louis Poirel, O.Olivier Vermorel and W.Wilca Villafana. A note on the strong parallel scalability of numerically scalable Poisson linear solvers.RR-9423Inria Bordeaux - Sud OuestSeptember 2021, 31
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• 30 reportO.Olivier Coulaud, A. A.Alain A. Franc and M.Martina Iannacito. Extension of Correspondence Analysis to multiway data-sets through High Order SVD: a geometric framework.RR-9429Inria Bordeaux - Sud-Ouest; InraeNovember 2021
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• 31 reportL.Luc Giraud, Y.-F.Yan-Fei Jing and Y.Yanfei Xiang. A block minimum residual norm subspace solver for sequences of multiple left and right-hand side linear systems.RR-9393Inria Bordeaux Sud-OuestFebruary 2021, 60
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• 32 reportE.Esragul Korkmaz, M.Mathieu Faverge, G.Grégoire Pichon and P.Pierre Ramet. Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization.RR-9396Inria Bordeaux - Sud Ouest2021, 16
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• 33 reportN.Nicolas Venkovic, P.Paul Mycek, L.Luc Giraud and O.Olivier Le Maitre. Recycling Krylov subspace strategies for sequences of sampled stochastic elliptic equations.RR-9425Inria Bordeaux - Sud OuestOctober 2021
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