2023Activity reportProjectTeamMEMPHIS
RNSR: 201521153G Research center Inria Centre at the University of Bordeaux
 In partnership with:Université de Bordeaux
 Team name: Modeling Enablers for MultiPHysics and InteractionS
 In collaboration with:Institut de Mathématiques de Bordeaux (IMB)
 Domain:Applied Mathematics, Computation and Simulation
 Theme:Numerical schemes and simulations
Keywords
Computer Science and Digital Science
 A6. Modeling, simulation and control
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.5. Multiphysics modeling
 A6.2.1. Numerical analysis of PDE and ODE
 A6.3.1. Inverse problems
 A6.3.2. Data assimilation
 A6.3.4. Model reduction
 A6.5.1. Solid mechanics
 A6.5.2. Fluid mechanics
 A9.2. Machine learning
Other Research Topics and Application Domains
 B2.2.1. Cardiovascular and respiratory diseases
 B4.2. Nuclear Energy Production
 B4.3.2. Hydroenergy
 B4.3.3. Wind energy
 B5.2.3. Aviation
 B5.2.4. Aerospace
 B5.5. Materials
1 Team members, visitors, external collaborators
Research Scientists
 Michel Bergmann [INRIA, Researcher, until Sep 2023, HDR]
 Michel Bergmann [INRIA, Senior Researcher, from Oct 2023, HDR]
 Michele Giuliano Carlino [ONERA, from Sep 2023]
 Alessia Del Grosso [INRIA, ISFP, from Nov 2023]
 Tommaso Taddei [INRIA, Researcher]
Faculty Members
 Angelo Iollo [Team leader, UNIV BORDEAUX, Professor, HDR]
 Afaf Bouharguane [UNIV BORDEAUX, Associate Professor]
PostDoctoral Fellows
 Umberto Bosi [INRIA, PostDoctoral Fellow]
 Antoine Fondaneche [INRIA, until Sep 2023]
 Birgul Koc [IFPEN, until Nov 2023]
 Nishant Kumar [INRIA]
PhD Students
 Eki Agouzal [EDF]
 Beatrice Battisti [ECOLE POLYT. TURIN, from May 2023]
 Maxime Chapron [ONERA]
 Jon Labatut [ONERA]
 Caroline AnnaLise Andrea Le Guern [IFPEN]
 Karl Maroun [UNIV POITIERS]
 Abdessamad Moussaddak [EDF, CIFRE, from Dec 2023]
 Thomas Philibert [ECOLE POLYT. TURIN]
 Michele Romanelli [ONERA]
 Ludovica Saccaro [INRIA, from Nov 2023]
 Alexis Tardieu [UNIV BORDEAUX]
 Mathias Truel [INGELIANCE, CIFRE, from May 2023]
Interns and Apprentices
 Mohamed Ben Abdelouahab [INRIA, from Feb 2023 until Jul 2023]
 Emanuela Dotti [INRIA, Intern, from Oct 2023]
 Elian Richard [INRIA, from Jun 2023 until Sep 2023]
 Pablo Solan Fustero [UNIV SARAGOSSE, from Mar 2023 until May 2023]
Administrative Assistant
 AnneLaure Gautier [INRIA, from Oct 2023]
Visiting Scientist
 Michele Giuliano Carlino [UNIV FERRARA, from Feb 2023 until Sep 2023]
External Collaborators
 Majdi Azaiez [Bordeaux INP, HDR]
 Astrid Decoene [UNIV BORDEAUX, from Dec 2023]
 Philippe Depouilly [CNRS, from Mar 2023]
 Francesco Fabbri [GSSI, from Oct 2023]
2 Overall objectives
2.1 Multiphysics numerical modeling
2.1.1 Reducedorder models: convergence between PDE models and data
Unprecedented opportunities exist to directly use already collected computational or experimental data to improve and build predictive models that can be used online for the simulation of parametric problems, robust design, and control in science and engineering. In this regard, our goal is to combine mechanistic causal models based on partial differential equations (PDEs) with large data sets to reduce the marginal cost of predictions.
Reducedorder models (ROMs) are our main tool for this purpose. ROMs are parametric mathematical models derived from the full set of PDEs using previously computed solutions. In many applications, the solution space turns out to be lowdimensional, so one can trade a minimal loss of accuracy for speed and scalability. ROMs counteract the curse of dimensionality by significantly reducing computational complexity.
Overall, ROMs have reached a certain level of maturity during the last decade, allowing their implementation in largescale industrial codes, mainly in structural mechanics. Nevertheless, some hard points stand. Parametric problems governed by strong advection fields or sensibly compactsupport solutions such as moving shocks suffer from a limited possibility of dimensional reduction and, at the same time, insufficient generalization of the model (outofsample solutions). The main reason for this is that the solution space is usually approximated by an affine or linear representation, which is intrinsically broad band for such problems.
We have worked on the development of model order reduction (MOR) techniques for nonlinear, advectiondominated problems, with emphasis on projectionbased Galerkin and PetrovGalerkin ROMs. First, we worked on the development of effective sampling strategies to reduce training costs. Second, we developed nonlinear, registrationbased approximation techniques, to overcome limitations of linear approximation methods (e.g., proper orthogonal decomposition, POD) to deal with strong advection fields. Third, we developed hybrid formulations that combine reducedorder and fullorder models to deal with complex flow features and/or complex parameterizations.
2.1.2 Schemes for Hierarchical meshes, multiphysics and asymptotic limits
The schemes we have developed aim at simulating complex multiphysics phenomena through appropriate PDE modeling, automatic implicit geometry representation (level sets), hierarchical Cartesian schemes (quadoctrees), parallel simulations, and accurate treatment of boundaries. Discretization schemes on hierarchical meshes allow multiscale solution of PDEs on nonbodyfitted meshes with a drastic reduction in computational setup overhead. The key idea is to use an octree mesh to approximate the solution fields, while the geometry is captured by level set functions. The boundary conditions are determined by appropriate interpolation methods to achieve sufficient accuracy. This approach eliminates the need for boundary conforming meshes, which require timeconsuming and errorprone mesh generation procedures, and opens the door to easy parallel simulation of very complex geometries.
One of the limitations of this approach is that a mesh with a fixed aspect ratio is not optimal for very anisotropic fields such as boundary layers. For such cases, we explored the idea of using a bodyfitted grid near the immersed obstacles and a hierarchical mesh in the background. Essentially, we use the techniques we have developed to impose boundary conditions on nonbodymatched meshes further from the boundary, where the solution is smoother and more isotropic. Our current investigations build on discontinuous Galerkin (DG) methods / ADER approaches to combine efficient interpolation strategies at the grid interfaces and compact reconstruction of the data at the grid level.
Part of our activity has been dedicated to improve schemes for all Mach number flows in both fluid dynamics and continuum mechanics. Phenomena of interest involve fluid flows and elastic materials whose deformations are investigated within a monolithic Eulerian framework. With this approach any material (gas, liquid or solid) can be described with the same system of conservation equations and a suitable general formulation of the constitutive law.
These schemes are accurate in computing steady state solutions as well as in approximating material wave propagation in various Mach regimes and different materials. We studied methods to overcome the need to solve for auxiliary relaxation variables while preserving the properties of the linearly implicit schemes. To achieve this, we split the stiff relaxation source terms from the fluxes and then reformulate the homogeneous part in an elliptic form. Further research on obtaining all Mach methods by including multidimensional knowledge in the numerical scheme is also being conducted. More specifically, we envisage to exploit a nodal pressure that depends on all the cells around the given node and naturally encompasses a consistent discretization of the divergence of the velocity vector.
3 Research program
Coherently with our investigation approach, we start from realworld applications to identify key methodological problems, then, we study those problems and develop new methods to address them; finally, we implement these methods for representative test cases to demonstrate their practical relevance.
3.1 Numerical models
We aim to further develop automated modelorder reduction (MOR) procedures for largescale systems in computational mechanics — here, automated refers to the ability to complete the analysis with minimal user intervention. First, we wish to combine nonlinear MOR with mesh adaptation to simultaneously learn rapid and reliable ROMs and effective highfidelity discretizations over a range of parameters. Second, we wish to develop componentbased MOR procedures to build interoperable components for steady and unsteady nonlinear PDEs: towards this end, we should develop efficient localized training procedures to build local ROMs for each archetype component, and also domain decomposition techniques to glue together the local models for prediction. We also wish to develop and analyze hybrid approaches that combine and merge firstprinciple models with datafit models, and also fullorder and reducedorder models for prediction of global engineering quantities of interest.
We envision that several methods that are currently developed in the team can be complemented by available tools from machine learning: representative examples include — but are not limited to — solution clustering, optimal sampling, classification. In this respect, a leap forward in industrial applications that we will pursue is without doubts the possibility of capitalizing on previous experience drawn from already acquired simulations to build nonintrusive models that combine nonlinear interpolations and nonlinear regression. New perspectives in this direction are offered by the Chair OneraNouvelle Aquitaine (cf. Regional initiatives).
As regards the work on numerical discretization of PDEs, compared to the previous evaluation, we focus on the representation of the solution in each computational cell by adopting a DG/ADER approach to improve the resolution of solution's discontinuities. This approach is complemented with a Chimera grid at the boundaries in order to improve accuracy by a body fitted mesh avoiding grid generation complexity for a general, possibly varying, geometrical topology. The thesis of Alexis Tardieu, which started in October 2021 and is funded by the University of Bordeaux, studies this approach.
In parallel, we continue our exploration of schemes in asymptotic regimes such as low and high Mach numbers for multimaterial flows. We aim for schemes that circumvent the problem of accuracy and time stepping in such regimes: the ultimate goal is to devise asymptoticpreserving schemes that are able to capture phenomena at the time scale of the fast waves and of the material waves with the same accuracy. For such a purpose, a new path based on numerical schemes with multidimensional knowledge is also being explored.
3.2 Applications
For energy applications, we will continue our investigations on wave energy converters and windturbines. Relative to wave energy converters, we are developing multifidelty models that couple the incompressible NavierStoke equations (NSE) around the floater with a Proper Orthogonal (POD) ROM or a simplifiedphysics model elsewhere.
 In October 2021, Nishant Kumar started a twoyear postdoctoral fellowship in the team, which was funded by the InriaIfpEN program; the aim is to couple an highfidelity model and a POD model based on the LES NavierStokes equations; the coupling is implemented in the SOWFA framework of OpenFOAM.
 In December 2021, Caroline Le Guern started her PhD in the team, in the framework of the InriaIfpEN program; Caroline works on the modeling and simulation of the fluidstructure interaction of nextgeneration windturbines with up to 250 meter rotor; the numerical implementation is based on the software Deeplines that is codeveloped by IfpEN.
 In April 2022, Umberto Bosi started a twoyear postdoctoral fellowship in the team, in collaboration with CARDAMOM: the project of Umberto, which was funded by Inria and the Region Nouvelle Aquitaine, focuses on the coupling between an highfidelity (e.g., NavierStokes) model and an asymptotic (e.g., shallow water or Boussinesq) model.
We are also collaborating with EDF to devise effective ROMs for parametric studies. In this collaboration, we emphasize the implementation of projectionbased ROMs for realworld applications exploiting industrial codes.
 In April 2021, Eki Agouzal started an industrial thesis to develop projectionbased ROMs for nonlinear structural mechanics problems in Code Aster, with emphasis on thermohydromechanical (THM) applications.
 In December 2023, Abdessamad Moussaddak started his PhD thesis on model reduction for river and coastal hydraulics.
Within the ARIA project, in collaboration with Nurea and the biomechanics lab of the Politecnico di Torino, we investigate the idea of data augmentation starting from a given aneurysm database. We construct statistically relevant synthetic aneurysms that can provide both heterogeneity and closeness to reality to test new biomarkers for aneurysm rupture. The thesis of Ludovica Saccaro funded by Inria is dedicated to this subject.
In the framework of the ANR DRAGON, we also increase our interactions with researchers in biology and physical science. in the center of biological studies in Chizé (centre d'études biologiques de Chizé). The ANR funds the PhD thesis of Karl Maroun at University of Poitiers.
The software development will be continued. We will pursue the development of the NEOS library: NEOS will be distributed in open source LGPL3.0. The HIWIND software will be rewritten based on NEOS library.
4 Application domains
4.1 Energy conversion
We apply the methods developed in our team to the domain of wind engineering and seawave converters. In Figure 1, we show results of a numerical model for a seawave energy converter. We here rely on a monolithic model to describe the interaction between the rigid floater, air and water; material properties such as densities, viscosities and rigidity vary across the domain. The appropriate boundary conditions are imposed at interfaces that arbitrarily cross the grid using adapted schemes built thanks to geometrical information computed via level set functions 44. The background method for fluidstructure interface is the volume penalization method 32 where the level set functions is used to improve the degree of accuracy of the method 4 and also to follow the object. The underlined mathematical model is unsteady, and three dimensional; numerical simulations based on a grid with $\mathcal{O}\left({10}^{8}\right)$ degrees of freedom are executed in parallel using 512 CPUs.
In the context of the Aerogust (Aeroelastic gust modelling) European project, together with Valorem, we investigated the behavior of wind turbine blades under gust loading. The aim of the project was to optimize the design of wind turbine blades to maximize the power extracted. A meteorological mast (Figure 2(a)) has been installed in March 2017 in Brittany to measure wind onsite: data provided by the mast have been exploited to initialize the mathematical model. Due to the large cost of the fullorder mathematical model, we relied on a simplified model 42 to optimize the global twist. Then, we validated the optimal configuration using the fullorder Cartesian model based on the NaSCar solver. Figure 2(b) shows the flow around the optimized optimized wind turbine rotor.
4.2 Schemes for turbulent flow simulations using Octrees
We have initially developed and tested a 3D firstorder Octree code for unsteady incompressible NavierStokes equations for full windmill simulations with an LES model and wall laws. We have validated this code on Occigen for complex flows at increasing Reynolds numbers. This step implied identifying stable and feasible schemes compatible with the parallel linear Octree structure. The validation has been conducted with respect to the results of a fully Cartesian code (NaSCAR) that we run on Turing (with significantly more degrees of freedom) and with respect to experimental results.
Subsequently, we have developed a secondorder Octree scheme that has been validated on Occigen for a sphere at a moderate Reynolds number ($\mathrm{Re}=500$), see Table 1. Then, for a cylinder at ($\mathrm{Re}=140000$) (Figures 3(a) and 3(b)), close to real applications, we have preliminary validation results for the secondorder scheme with respect to experimental drag coefficient (Table 2). Additional resources will be asked on Occigen to complete the study.
Mesh  $\Delta {x}_{\mathrm{min}}$  number of cells  ${C}_{\mathrm{D}}$ (1storder scheme)  ${C}_{\mathrm{D}}$ (2ndorder scheme) 
1  $0.094$  $0.72\xb7{10}^{5}$  N.A.  $0.526$ 
2  $0.047$  $4.9\xb7{10}^{5}$  $0.595$  $0.522$ 
3  $0.023$  $4.7\xb7{10}^{6}$  $0.546$  $0.492$ 
4  $0.012$  $37.6\xb7{10}^{6}$  $0.555$  $0.496$ 
Case  ${C}_{\mathrm{D}}$ 
Octree, 1storder scheme  $1.007$ 
Octree, 2ndorder scheme  $1.157$ 
Cartesian  $1.188$ 
Experimental estimate 35  $1.237$ 
4.3 Vascular flows
A new research direction pursued by the team is the mathematical modelling of vascular blood flows in arteries. Together with the startup Nurea and the surgeon Eric Ducasse, we aim at developing reliable and automatic procedures for aneurysm segmentation and for the prediction of aneurysm rupture risk. Our approach exploits two sources of information: (i) numerical simulations of blood flows in complex geometries, based on an octree discretization, and (ii) computed tomography angiography (CTA) data. Figure 4 shows the force distribution on the walls of the abdominal aorta in presence of an aneurysm; results are obtained using a parallelized hierarchical Cartesian scheme based on octrees.
Further information is given in the sections dedicated to the new results.
4.4 Fluidstructure interactions using Eulerian nonlinear elasticity models
Mathematical and numerical modeling of continuum systems undergoing extreme regimes is challenging due to the presence of large deformations and displacements of the solid part, and due to the strongly nonlinear behavior of the fluid part. At the same time, proper experiments of impact phenomena are particularly dangerous and require expensive facilities, which make them largely impractical. For this reason, there is a growing interest in the development of predictive models for impact phenomena.
In MEMPHIS, we rely on a fully Eulerian approach based on conservation laws, where the different materials are characterized by their specific constitutive laws, to address these tasks. This approach was introduced in 39 and subsequently pursued and extended in 43, 38, 33, 34 and 9. In Figure 5, we show the results of the numerical simulation of the impact of a copper projectile immersed in air over a copper shield. Results are obtained using a fully parallel monolithic Cartesian method, based on a ${4000}^{2}$ fixed Cartesian grid. Simulations are performed on a cluster of 512 processors, and benefits from the isomorphism between grid partitioning and processor topology.
In figure 6, we show the results of a three dimensional simulation of a cardiac pump (LVAD, left ventricule assisted device).
5 Social and environmental responsibility
As discussed in the previous section, we are particularly interested in the development of mathematical models and numerical methods to study problems related to renewable energies, and ultimately contribute to nextgeneration sustainable solutions for energy extraction.
5.1 Impact of research results
We are studying two types of green energy extractors: wave energy converters (WECs) and wind energy.
As regards WECs, we are working with the PoliTO (Torino, Italy) to model the behavior of inertial sea wave energy converters (ISWEC), and we are also working with a Bordeauxbased startup for another device to extract energy from waves via an InriaTech project and a NouvelleAquitaine Regional Project submitted by Memphis in collaboration with the CARDAMOM team.
As regards wind energy, we focus on the analysis of wind turbines. In the past, we have supervised two PhD CIFRE theses with VALOREMValeol, and are currently working with them in a European RISE ARIA project led by Memphis. We also work with IFPEN on the aeroelastic modeling of large wind turbines and the study and optimization of turbines farms in the framework of the joint laboratory InriaIFPEN with a thesis funded by IFPEN and a postdoc funded by Inria (which started in October 2021).
In conjunction with these activities, in collaboration with ANDRA (the national agency for storage of nuclear waste), we investigated the development of reducedorder models to allow efficient and accurate simulations for deep geological storage planning. This activity was the subject of the PhD thesis of Giulia Sambataro who successfully defended her PhD thesis in December 2022.
6 Highlights of the year
Model order reduction by convex displacement interpolation.
In 31, Cucchiara et al. extended the nonlinear interpolation technique of 41 to deal with multidimensional parameter domains and with datasets of several snapshots. The method of 41, which is dubbed convex displacement interpolation (CDI), relies on optimal transportation to perform accurate nonlinear interpolations between two solution snapshots. The method of 31 combines a boundaryaware registration procedure with a regression technique to properly exploit datasets with more than two snapshots for interpolation and to cope with multidimensional parameter domains.
During the training (offline) stage, the method in 31 exploits a feature extraction technique to identify point clouds for each snapshot in the training set; then, it relies on a pointset registration technique to match point clouds for different snapshots; during the prediction (online) stage, we first rely on a regression algorithm to predict the position of the point cloud; then, we apply a boundaryaware registration technique to define bijective mappings that deform the new point cloud into the point clouds of the neighboring elements of the dataset, while preserving the boundary of the domain; finally, we define the estimate as a weighted combination of modes obtained by composing the neighboring snapshots with the previouslybuilt mappings. We demonstrate the accuracy of the method through the vehicle of several numerical examples for compressible and incompressible, viscous and inviscid flows. Furthermore, we employ the nonlinear interpolation procedure to augment the dataset of simulations for linearsubspace projectionbased model reduction: our data augmentation procedure is designed to reduce offline costs (which are dominated by snapshot generation) of model reduction techniques for nonlinear advectiondominated problems.
In Figure 7, we illustrate the performance of the method for the compressible flow past a RAE2822 airfoil for varying inflow Mach number and angle of attack. Figures 7(a) and (b) show the behavior of the pressure coefficients for two different parameter values; Figures 7(c) and (d) show the prediction of the pressure coefficient on lower (LOW) and upper (UP) sides of the blade of linear and nonlinear interpolation for an outofsample configuration. We notice that the nonlinear interpolation strategy is quantitively and qualitatively more accurate than the linear counterpart, for the same amount of offline datapoints.
7 New software, platforms, open data
7.1 New software
7.1.1 COCOFLOW

Keywords:
3D, Elasticity, MPI, Compressible multimaterial flows

Functional Description:
The code is written in fortran 95 with a MPI parallelization. It solves equations of conservation modeling 3D compressible flows with elastic models as equation of state.
 URL:

Authors:
Alexia De Brauer, Florian Bernard, Yannick Gorsse, Thomas Milcent, Angelo Iollo

Contact:
Florian Bernard

Partners:
CNRS, Université Bordeaux 1
7.1.2 KOPPA

Name:
Kinetic Octree Parallel PolyAtomic

Functional Description:
KOPPA is a C++/MPI numerical code solving a large range of rarefied flows from external to internal flows in 1D, 2D or 3D. Different kind of geometries can be treated such as moving geometries coming from CAO files or analytical geometries. The models can be solved on Octree grids with dynamic refinement.
 URL:

Contact:
Angelo Iollo

Participant:
Florian Bernard
7.1.3 NaSCar3D

Name:
NavierStokes Cartesian 3D

Keywords:
HPC, Numerical analysis, Fluid mechanics, Langage C, PETSc

Scientific Description:
NaSCar can be used to simulate both hydrodynamic biolocomotion as fish like swimming and aerodynamic flows such wake generated by a wind turbine.

Functional Description:
This code is devoted to solve 3Dflows in around moving and deformable bodies. The incompressible NavierStokes equations are solved on fixed grids, and the bodies are taken into account thanks to penalization and/or immersed boundary methods. The interface between the fluid and the bodies is tracked with a level set function or in a Lagrangian way. The numerical code is fully second order (time and space). The numerical method is based on projection schemes of ChorinTemam's type. The code is written in C language and use Petsc library for the resolution of large linear systems in parallel.
NaSCar can be used to simulate both hydrodynamic biolocomotion as fish like swimming and aerodynamic flows such wake generated by a wind turbine.
 URL:

Contact:
Michel Bergmann

Participant:
Michel Bergmann

Partner:
Université de Bordeaux
7.1.4 NSpenal

Name:
NavierStokespenalization

Keywords:
3D, Incompressible flows, 2D

Functional Description:
The software can be used as a black box with the help of a data file if the obstacle is already proposed. For new geometries the user has to define them. It can be used with several boundary conditions (Dirichlet, Neumann, periodic) and for a wide range of Reynolds numbers.

Contact:
CharlesHenri Bruneau

Partner:
Université de Bordeaux
7.1.5 HiWind

Keyword:
Simulation

Functional Description:
Hiwind is a software that allows to model in 2D and 3D the effects of air flow on a wind turbine blade (moving solid or elastic structures), and to simulate numerically their interactions. Hiwind also allows to model and characterize the abnormal behavior to warn about a potential weakening of the structure. Hiwind is a "drag and drop" solution (automated meshing phase), massively parallel, and uses adaptive meshing.

Authors:
Claire Taymans, Angelo Iollo, Michel Bergmann

Contact:
Angelo Iollo

Partner:
Valeol
7.1.6 NEOS

Keyword:
Octree/Quadtree

Functional Description:
NEOS is a software framework for numerical modeling of multiphysical problems on hierarchical Cartesian meshes (quadtree in 2D and octree in 3D). It is mainly based on the bitpit library (https://optimad.github.io/bitpit/). NEOS provides :  the creation and parallel management of hierarchical Cartesian meshes (2D quadtree or 3D octree)  global or local mesh refinement (based on a distance of levelset or other physical criteria)  the management of several moving geometries in an analytical or explicit form (STL files or others)  the calculation of geometries levelsets at any point of the mesh  2D/3D differential operators of (gradient, laplacian, hessian, ...)  various 2D/3D interpolators (bilinear, radial basis functions RBF)  an API for solvers (currently with PETSC)  a complete Python3 interface

Authors:
Angelo Iollo, Michel Bergmann, Philippe Depouilly, Laurent Facq, Antoine Fondaneche, Florian Bernard, Antoine Gerard, Matías Hastaran

Contact:
Michel Bergmann

Partner:
CNRS
8 New results
8.1 Componentbased model order reduction for radioactive waste management
Participants: Angelo Iollo, Giulia Sambataro, Tommaso Taddei.
At the end of their cycle, radioactive materials are placed in arrays of cylindrical boreholes (dubbed alveoli) deep underground; due to the large temperatures of the radioactive waste, the thermal flux generated by the alveoli drives a complex timedependent phenomenon which involves the thermal, hydraulic and mechanical (THM) response of the medium. The role of simulations is to predict the longterm system response and ultimately assess the impact of the repository site to the surrounding areas: Figure 8(a) shows a typical system configuration considered for numerical investigations.
Due to the complex nature of the equations (a system of five coupled nonlinear timedependent threedimensional equations) and due to the uncertainty in several parameters of the model and on boundary conditions, MOR techniques are important to reduce the computational burden associated with thorough parametric studies. In particular, it is important to study the system behavior for different numbers of alveoli: it is possible to show that changing the number of alveoli induces a change in the topology of the problem and thus prevents the application of standard monolithic MOR techniques developed for fixed domains or diffeomorphic families of parametric domains. We should thus devise componentbased MOR procedures that are compatible with topology changes.
The PhD project of Giulia Sambataro aimed to devise a rapid and reliable componentbased MOR technique for THM systems, for radioactive waste management applications. During the first year of her PhD, Giulia developed a monolithic MOR technique for THM systems which relies on a PODGreedy algorithm to sample the parameter domain and to hyperreduction based on empirical quadrature to reduce online prediction costs. During the second and third year, Giulia developed a componentbased MOR formulation — which is dubbed oneshot overlapping Schwartz (OS2) method — for nonlinear steady PDEs and finally she extended the approach to THM systems with varying numbers of alveoli.
Giulia successfully defended her PhD thesis in December 2022; her work led to the publication of two articles on peerreviewed journals, 40 and 15. Figure 8(b) shows the temporal behavior of the HF and predicted pressure and temperature in a select point in the proximity of one alveolus for an outofsample configuration. We observe that the ROM is able to adequately predict the solution behavior; in our numerical experiments, we experienced an average 20x speedup over the range of configurations.
8.2 Registration methods for advectiondominated PDEs
Participants: Angelo Iollo, Tommaso Taddei.
A major issue of stateoftheart MOR techniques based on linear approximation spaces is the inability to deal with parameterdependent sharp gradients, which characterize the solutions to advectiondominated problems. To address this issue, we propose a registration technique to align local features in a fixed reference domain. In computer vision and pattern recognition, registration refers to the process of finding a transformation that aligns two datasets; here, registration refers to the process of finding a parametric spatiotemporal transformation that improves the linear compressibility of the solution manifold.
A registration procedure has been proposed in 45 and then further developed in 47, 46, 36. In particular, in 47, we considered the application to onedimensional applications in hydraulics; in an ongoing collaboration with EDF, we aim to extend the approach to twodimensional steady and unsteady problems. Figure 9 shows results for a SaintVenant problem (flow past a bump): Figures 9(a) and 9(b) show the free surface $z$ for two different parameters and two time instants, while Figure 9(c) shows the behavior of the outofsample projection error associated with a snapshotbased POD space with and without registration. We observe that registration is key to improve performance of linear compression strategies such as POD.
In 41, Iollo and Taddei proposed a general (i.e., independent of the underlying PDE) nonlinear interpolation technique based on optimal transportation of Gaussian models of coherent structures of the flow.
In 31, Cucchiara et al. extended such a technique to deal with multidimensional parameter domains and with datasets of several snapshots. The method of 41 relies on optimal transportation to perform accurate nonlinear interpolations between two solution snapshots. The method of 31 combines a boundaryaware registration procedure with a regression technique to properly exploit datasets with more than two snapshots for interpolation and to cope with multidimensional parameter domains. See the Highlights section 6 for more information.
8.3 Aortic aneurysms: automatic segmentation and registration
Participants: Angelo Iollo, Gwlady Ravon, Sebastien Riffaud, Ludovica Saccaro.
In 37, we developed a new artificial neural network to automatically segment aortic aneurysm. The main idea with this approach was to consider each pixel of the image individually and to see if a model could learn how to categorize it as lumen only from its own intensity and the intensity of its 26 neighbors. We tested different inputs (values, means, variances...) and architectures: a sequential model was retained. For the input, each sample is a vector of 27 intensity values. Only pixels whose intensity is between 100 and 700 are kept for training and prediction.
The second axis of development concerned registration. In her PhD, Ludovica Saccaro presents several complete and automated working pipelines for clinical applications, for the pathology of abdominal aortic aneurysm. Her work is based on a mathematical modeling of aneurysm geometry, used for registration, risk assessment using a reduced modeling approach, and a generative algorithm. First, she introduced the geometric modeling technique, using Bspline functions and Fourier series for modeling. The geometric modeling presented in this work ensures the isolation of the aortic vessel, even in the presence of secondary vessels, while smoothing and regularizing its shape. The entire modeling process is automated, making it a crucial step for clinical support in aneurysm pathology. It aims to ensure that different geometrical shapes are comparable in a mathematical sense. To highlight the practical application, she integrated the modeling into a registration pipeline for clinical diagnosis and followup, providing automated tools for quantitative measurement and qualitative indication of disease progression by mathematically standardizing the aneurysm shape. Looking ahead, the registration pipeline could track the entire pathology, enabling close monitoring of patientspecific aneurysm evolution for valuable data in population studies, prevention and surgical planning. Then, she extended the use of the modeling as a basis for hemodynamic simulations, aiming to create a pipeline for constructing a projection space to assess abdominal aneurysm risk. The space created is meant to be used in a predictive sense, namely to derive hemodynamical quantities solely from geometry, to maintain the patientspecific approach, and on a dataset of previous simulations. The same procedure could be applied to other indicators, such as the pressure field or the WSS, as the choice of the indicator does not impact any steps in the proposed procedure, which remains a key achievement of our work. The limited accuracy of the approximated fields is partly due to the lack of a large amount of data, and the absence of personalized boundary conditions for each patient. In this context, she also proposed an automated pipeline that starts from the geometrical modeling and outputs synthetic aneurysm shape, by creating a mathematical space for modeling aortic aneurysms, using reducedorder model techniques. This part of the work is of interest since in clinical settings datasets are often scarce, and synthetic data emerged as a promising solution.
The PhD thesis of Ludovica Saccaro is expected to be defended in February 2023. A paper is in preparation.
8.4 Model reduction for aerodynamic applications
8.4.1 Deep learning wall laws for aerodynamic simulations
Participants: Michel Bergmann, Thomas Philibert, Angelo Iollo, Michele Romanelli.
The availability of reliable and accurate wall laws is one of the main challenges of modern Computational Fluid Dynamics (CFD). Wall models are mandatory for the application of largescale turbulence (LES) simulations for flows representative of aeronautical applications, and they are also indispensable for ReynoldsAveragedNavierStokes (RANS) simulations, either when using immersed boundary methods (IBM) methods, or for the implementation of light calculations useful for parametric studies, flow control or shape optimization, where multiples simulations are often required and the cumulative computational cost can become prohibitive. Wall laws help to lighten the computational load by replacing the resolution of the parietal flow (typically the most densely meshed zone) with a model. Given the complexity of phenomena that can be modeled thanks to the flexibility of neural networks neural networks, these methods show undeniable potential in their application to the modelling of flows.
The research objective is to propose a wall law based on deep learning algorithms applicable within the framework of ReynoldsAveragedNavierStokes (RANS) simulations, outperforming conventional models in terms of accuracy and generality. In addition, the exploratory nature of this study aims to identify input quantities that would enable more reliable modeling of boundary layer development. A novel approach inspired by the DirichlettoNeumann map is proposed, directly imposing viscous flow across the interface between the modeled region and RANS calculations. This involves a model composed of two interconnected neural networks: the first estimating viscous shear stress, and the second evaluating the wallnormal derivative of the velocity field. Both neural networks are trained using dimensionless data extracted from RANS simulations of flow over 2D bumps. Evaluating the model's performance involves comparing simulations with wall modeling to fullysolved calculations for flow configurations (over bumbs and airfoils) not encountered during neural network training. The robustness and accuracy of the wall model are evident in testing, demonstrating an ability to reproduce the friction coefficient with only a minimal error across all tested cases.
8.4.2 Clustered active subspaces for aerodynamic shape optimisation
Participants: Michel Bergmann, Maxime Chapron.
Shape optimisation has seen an increase of the number of design variables used, with finer geometry control enabling more precise results. However, this increase in dimensionality complexifies an already tough to optimise function such as drag. Gradientbased optimisers are powerful but local, and do not guarantee convergence towards the global optimum. On the other end of the spectrum, surrogatebased optimisation techniques are good global optimisers, but struggle in highdimensional design spaces, due to the curse of dimensionality. Dimension reduction provides answers to this particular problem, and the Active Subspaces method has been shown to be a viable option, with the benefit of using gradient information to discover influential design parameters. We take Active Subspaces further by using a combination of them to identify linear manifolds in subregions of the design space, instead of trying to identify a single global trend. We are then free to train local surrogate models inside of these locally reduced spaces, where the reduced number of points and dimensions renders their training feasible. More specifically, the global surrogate modelling methodology was improved by paying special attention to the areas surrounding the boundaries between clusters 22. We defined overlapping zones between clusters by computing Euclidean distances to explicit cluster boundaries given by a nonlinear Support Vector Classifier. Data points within these zones are mutualised between neighbouring clusters, yielding improved accuracy near boundaries by reducing the need for local surrogate models to extrapolate. This was done to improve model accuracy without adding new data points, as well as to reduce uncertainty around these areas in order to prevent the Efficient Global Optimisation (EGO) procedure from wanting to add points in these areas, instead of near known minima.
The latter part of the year saw contributions to the EGO methodology, with the implementation of a stopping criterion based on estimations of the true, unknown minimum. Compared to usual EGO procedures which are carried out until a given computational budget runs out, this criterion allows an estimation of EGO performance in real time, and allows (for example) the switch to gradient descent once a certain level of convergence has been reached, drastically reducing the number of function evaluations needed to converge. We have also made improvements to the infill criterion maximisation methodology, further increasing efficiency. A paper on the EGO methodology is in preparation.
8.5 Projectionbased model order reduction for parametric quasistatic nonlinear mechanics using an opensource industrial code
Participants: Eki Agouzal, Michel Bergmann, Tommaso Taddei.
In 11, we proposed a projectionbased model order reduction procedure for a general class of parametric quasistatic problems in nonlinear mechanics with internal variables; the methodology is integrated in the industrial finite element code Code Aster. We developed an adaptive algorithm based on a PODGreedy strategy, and we developed an hyperreduction strategy based on an elementwise empirical quadrature, in order to speed up the assembly costs of the ROM by building an appropriate reduced mesh. We introduced a costefficient error indicator which relies on the reconstruction of the stress field by a GappyPOD strategy. We presented numerical results for a threedimensional elastoplastic system in order to illustrate and validate the methodology.
This approach was then extended to a multimodeling industrial testcase 25. More specifically, we looked at a standard section of a power plant containment, consisting of reinforced concrete. Such numerical simulations involve a multimodeling approach: a threedimensional nonlinear thermohydroviscoelastic rheological model is used for concrete; and prestressing cables are described by a onedimensional linear thermoelastic behavior. The methodology is validated on the fields and quantities of interest specific to engineers for this type of problem, on a mesh used in realworld engineering simulations.
8.6 Efficient Simulation of Wave Energy Converters
Participants: Beatrice Battisti, Michel Bergmann, Umberto Bosi, Giovanni Bracco, Martin Parisot.
In response to the evolving energy landscape, the marine sector is exploring wave energy converters (WECs) for clean energy generation. The deployment of WECs in farms is crucial for achieving commercialscale production, necessitating preliminary numerical simulations due to complex hydrodynamics. Although conventional highfidelity simulations are resourceintensive, they are essential for accurately capturing the complexities of highly nonlinear phenomena.
On the one hand, Beatrice Battisti (PhD student), Giovanni Bracco and Michel Bergmann works on a methodology that integrates a highfidelity solver (CFD) for the nearfield representation of floaters with a ReducedOrder Model (ROM) for farfield wave propagation. Information exchange between the two models occurs bidirectionally. From the CFD to the ROM models, information passes through the violet zones in Figure 13: a minimization problem is solved to determine the ROM solution that best approximates the highfidelity solution in that region. Subsequently, the ROM solution is transmitted to the CFD as highfidelity boundary conditions, considering the incoming wave. Through testing under various flow conditions and with a floating body, this methodology demonstrates accurate flow reconstruction and a comprehensive description of floater dynamics. In Figure 14, translations and forces acting on the body are depicted. The coupled model results (hf+POD) are illustrated for an insample reconstruction and an outofsample case, where snapshots from simulations of two different waves are utilized to obtain results for the test wave. The reference is the outcome from the highfidelity simulation of the test wave across the entire domain (HF). The coupled model significantly reduces computational costs, thereby streamlining optimization and design processes for wave energy converter farms. One paper is in preparation.
On the other hand, Umberto Bosi (postdoc), Michel Bergmann and Martin Parisot (Inria CARDAMOM) proposed a novel approach to simulate wave energy converters and their interactions with wave dynamics (paper in preparation). It couples a low performance, high fidelity Navier Stokes (NS) model that simulated the converter with the faster performances of asymptotic models such as Boussinesq (B) models for wave propagation. This approach allows to well capture the highly nonlinear and complex effects close to the structure thanks to the NS model and efficiently propagate the waves between structures such that even wave energy converters farm can be simulated precisely. They have demonstrated that their coupling approach, inspired by the perfectly matched layer technique, permits the transmission of waves from the B domain to the NS one without loss of informations. Moreover, reproducing the experiences of Beji and Battjes (1993) and Liu et al. (2019) of wave passing over a submerged hill, they have shown that the resulting waves preserve more informations on nonlinearities that a non coupled Boussinesq model.
9 Bilateral contracts and grants with industry
9.1 Bilateral contracts with industry
 Contrat accompagnement Cifre Ingeliance (M. Truel)  du 01/05/2023 au 30/04/2026
 Contrat accompagnement EDF (E. Agouzal)  du 01/04/2021 au 30/03/2024
 Contrat accompagnement IFPEN (C. Le Guern)  du 01/12/2021 au 30/11/2024
10 Partnerships and cooperations
10.1 International initiatives
10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program
Participants: Michel Bergmann, Angelo Iollo, Tommaso Taddei.
MARE
 Title: Multiscale Accurate Reducedorder model Enablers
 Duration: 20192023
 Coordinator: Charbel Farhat (cfarhat@stanford.edu)
 Partner: Stanford University Stanford (United States)
 Inria contact: Angelo Iollo
 Summary: Reducedorder models (ROMs) are simplified mathematical models derived from the full set of partial differential equations governing the physics of the phenomenon of interest. We focus on ROMs that are datadriven as they are based on relevant solution data previously obtained. In particular we will focus on multiscale adaptive models where the large scales are governed by a PDE and the small scales are described by data driven models. To do that we will leverage on tools from data geometry, numerical PDEs and machine learning.
10.2 International research visitors
10.2.1 Visits of international scientists
Michele Giuliano Carlino, University of Ferrara, from February 2023 to September 2023.
10.3 European initiatives
10.3.1 H2020 projects
ARIA
ARIA project on cordis.europa.eu

Title:
Accurate Roms for Industrial Applications

Duration:
From December 1, 2019 to November 30, 2024

Partners:
 INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE (INRIA), France
 ESTECO SPA (ESTECO), Italy
 NUREA, France
 VALOREM SAS (valorem), France
 SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE (SISSA), Italy
 IEFLUIDS S.R.L., Italy
 POLITECNICO DI TORINO (POLITO), Italy
 POLITECNICO DI MILANO (POLIMI), Italy
 OPTIMAD ENGINEERING SRL (Optimad srl), Italy
 UNIVERSITY OF SOUTH CAROLINA (USC), United States
 VOLKSWAGEN AKTIENGESELLSCHAFT (VW AG), Germany
 VIRTUALMECHANICS SL (VM), Spain
 VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY (VT), United States
 UNIVERSITA CATTOLICA DEL SACRO CUORE (UCSC), Italy
 BOARD OF TRUSTEES OF THE LELAND STANFORD JUNIOR UNIVERSITY (STANFORD), United States
 UNIVERSIDAD DE SEVILLA, Spain

Inria contact:
Angelo IOLLO

Summary:
The project Accurate Roms for Industrial Applications aims at developing an array of mathematical methods for constructing predictive reducedorder models (ROMs) with guaranteed accuracy, robustness, reliability and efficiency for applications involving complex physical phenomena. New approaches to this challenge are proposed here with a focus on the Euler and Navier–Stokes equations of fluid flow, two of the most challenging continuum models with an extraordinary rich range of industrial applications. The mathematical modeling and solution of the Euler and NavierStokes equations is sometimes cited as the greatest challenge in continuum modeling of physical phenomena. This topic is selected as our principal focus because of its intrinsic importance, but also because the mathematical methods developed in addressing this very challenging task may well have an impact on other fields of knowledge. We plan to tackle these challenging objectives in this staff exchange program by combining the unique expertise of our extended research team whose members have made significant progress in ROM research during the past decade. This academic expertise is crossfertilized by the exchange with knowledge intensive SMEs ans start up and well established industrial partners that will benefit from the scientific and technological results of the team and will challenge the solutions found with applications in real world problems.
10.4 National initiatives

ANR (national agency for research funding)
DRAGON2.
 Principal investigators: Michel Bergmann.
 Partners: CNRS/Université de Poitiers/Inria. 27 k€+ 1 PhD.
 Summary: The goal is study the aquatic swimming a several snakes using biomimetism and bioinspiration. In this project, we have experimental data for snake swimming, and we are building a numerical twin to compute integral quantities like the efficiency. Reinforcement learning is also considered to optimize the snake swimming.

ANR (national agency for research funding)
RedLum.
 Principal investigators: Tommaso Taddei.
 Partners: Team ACTA at INRAE Rennes.
 Summary: REDLUM is a joint project between the team ACTA at INRAE Rennes and the team MEMPHIS at Inria Bordeaux; the project will fund a PhD thesis in October 2024: the selected student will join team MEMPHIS in Bordeaux and will work closely with the other partners of the project. The objective of REDLUM is to develop a model reduction procedure for turbulent flows with unknown boundary conditions; the ultimate goal is to devise a rapid and reliable simulation tool to tackle realtime data assimilation tasks in agricultural sciences. The distinctive methodological feature of the approach that we wish to develop is a stochastic closure model to adequately approximate the dynamics of the lowdimensional coherent structures of the system.

Inria Exploratory Action: AM2OR (Adaptive meshes for model order reduction).
 Principal investigators: Nicolas Barral (Inria team: Cardamom), Tommaso Taddei. 14 k€+ 1 PhD + 1 PostDoc.
 Summary: Mesh adaptation and model order reduction both aim at reducing significantly the computational cost of numerical simulations by taking advantage of the solution's features. Model order reduction is a method that builds lighter surrogate models of a system's response over a range of parameters, which is particularly useful in the solution of design and optimization inverse problems. Reducedorder models rely on a highfidelity (e.g., finite element) approximation that should be sufficiently accurate over the whole range of parameters considered: in presence of structures such as shocks and boundary layers, standard mesh refinement techniques would lead to highfidelity models of intractable size. In this project, we propose a novel adaptive procedure to simultaneously construct a highfidelity mesh (and associated discretisation) and a reducedorder model for a range of parameters, with particular emphasis on inverse problems in computational fluid dynamics.
10.5 Regional initiatives
Chaire OneraNouvelle Aquitaine PROpulsion Verte (PROVE)
 Duration: 20222027

Summary: The Chair is dedicated to the development of reduced models at the crossroads between PDE modelling and machine learning, with application to aerodynamics for propulsion. The Chair has 6 PhD students, 2 postdocs and a budget for research activities (internships, missions). 4 theses have already been launched. The Chair has a budget of 1.2M€.
The project is led by Dr. Denis Sipp at ONERA and Prof. Angelo Iollo at INRIA Bordeaux.
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
Michel Bergmann, Angelo Iollo and Tommaso Taddei organized the ARIA 1st Workshop in Bordeaux from 08/03/2023 to 10/04/2023. The workshop was on Reduced Order Models and aimed to progress towards key advances in modeling multiscale nonlinear physical phenomena. This workshop was supported by: the European Commission, Inria Bordeaux, CNRS and Bordeaux University.
Michel Bergmann organized the minisymposium "Advances in embedded and Eulerian methods for fluidstructure interaction" at ICIAM, Tokyo.
11.1.2 Invited talks
 Michel Bergmann: January 16. An overview of current research in model order reduction at INRIA. Seminar at Sandia Livermore.
 Alessia Del Grosso: November 28. From hypersonic to low Mach flows using multipoint numerical methods. Strasbourg. Seminar at IRMA.
 Alessia Del Grosso: December 5. Entropy stable, positivity preserving and wellbalanced multipoint schemes for 2D shallow water system. Chai du Château d’Eyran. Journée du LRC Anabase.
 Angelo Iollo: March 15. Discussion of Some Examples of Linear or Nonlinear, Intrusive or Nonintrusive Reduced Models based on Convex Displacement Interpolation. Paris. Seminar at SafranTech.
 Angelo Iollo: November 21. Retour sur la publication "Enablers for robust POD models" (Bergmann, Bruneau, Iollo, JCP, 2009): Pourquoi j’ai changé d’avis sur tout ou presque. Paris. Seminar at CNAM.
 Angelo Iollo: November 2224. Model Reduction by Convex Displacement Interpolation. ParisSaclay. Mortech conference.
11.2 Teaching  Supervision  Juries
11.2.1 Teaching
Two members of the team are Professor (Angelo Iollo) or Assistant Professor (Afaf Bouharguane) at Université de Bordeaux and have teaching duties, which consist in courses and practical exercises in numerical analysis and scientific computing. Michel Bergmann (CR) also teaches around 64 hours per year (practical exercises in programming for scientific computing). Tommaso Taddei (CR) also teaches around 50 hours per year (practical exercises in numerical analysis and scientific computing).
11.2.2 Supervision
 20212024. Eki Agouzal, Cifre (Industrial thesis), EDF. Estimation de l’état mécanique d’enceintes de confinement par assimilation de données provenant de la maquette Vercors. Advisors: Michel Bergmann, Tommaso Taddei.
 20202023. Beatrice Battisti, Politecnico di Torino. Multifidelity multiscale numerical modelling of wave energy converters farms. Advisors: Michel Bergmann, Giovanni Bracco.
 20222025. Maxime Chapron, ONERA. Active Subspaces for Dimension Reduction Applied to Aerodynamic Shape Optimisation. Advisor: Michel Bergmann.
 20222025. Jon Labatut. Bourse Onera. Interpolation de déplacement convexe. Advisors: Angelo Iollo, Tommaso Taddei.
 20212024. Caroline Le Guern, Ifpen. Modelisation de l’aeroelasticité en grandes transformations par un couplage partitioné: application aux grandes eoliennes. Advisor: Michel Bergmann.
 20212024. Karl Maroun, Université de Poitiers (ANR Dragon2). Biomimetism and bioinspiration of a snakes’s anguilliform swimming: numerical twin and machine learning. Advisors: Michel Bergmann, Philippe Traoré.
 20232026. Abdessamad Moussaddak, thèse CIFRE EDF. Model reduction for river and coastal hydraulics. Advisors: Astrid Decoune, Angèlique Ponçot, Tommaso Taddei.
 20202023. Thomas Philibert. Bourse Politecnico di Torino. Convergence entre modèles et données pour la simulation d’écoulements turbulents en propulsion aéronautique. Advisors: Angelo Iollo, Francesco Larocca.
 20212024. Michele Romanelli, Chaire ONERA. Lois de Paroi à Apprentissage Profond pour Simulations Aérodynamiques. Advisors: Héloïse Beaugendre, Michel Bergmann.
 20202023. Ludovica Saccaro. Bourse Inria. Identification de biomarqueurs mécaniques pour l’évaluation du risque de rupture d’anévrismes aortiques abdominaux. Advisors: Angelo Iollo.
 20212024. Alexis Tardieu. Bourse ministère. DG sur maillage hierarchique. Advisors: Afaf Bouharguane, Angelo Iollo.
 20222025. Ishak Tifouti, Inria Exploratory Action, AM2OR project. Registrationbased model reduction with mesh adaptation. Advisors: Nicolas Barral, Tommaso Taddei.
 20232026. Mathias Truel. Thèse CIFRE Ingeliance. Modèles hybrides instationnaires pour l’interaction fluide structure. Advisors: Michel Bergmann, Angelo Iollo.
11.2.3 Juries
Angelo iollo: Reviewer of the PhD thesis of Paola Allegrini (Institut de Mathématiques de Toulouse) 20/09/23. President of the HDR jury of Laurent Monasse (Nice) 12/20/23. Member of the PhD jury of Stefano Piccardo (Université Polytechnique de Catalogne) 04/12/23. Member of the Jury Chaire Calcul Scientifique CNAM, Paris, 04/23. Member of the Jury Concours CR INRAE, 04/23. Member of the Comité de recrutement Ingénier de recherche Onera, 04/23.
Michel Bergmann: Reviewer of the PhD thesis of Yohan Poirier (Ecole centrale de Nantes).
11.3 Popularization
11.3.1 Internal or external Inria responsibilities
Michel Bergmann has been promoted to DR2 (senior researcher).
Angelo Iollo. Named to the departmental council of "Sciences du Numérique et Ingénierie" of the University of Bordeaux. 20192023.
12 Scientific production
12.1 Major publications
 1 articleAn allspeed relaxation scheme for gases and compressible materials.Journal of Computational Physics3512017, 124HALDOI
 2 articleFluidsolid Floquet stability analysis of selfpropelled heaving foils.Journal of Fluid Mechanics9102021, A28HALDOI
 3 articleEnablers for robust POD models.Journal of Computational Physics22822009, 516538
 4 articleAn accurate cartesian method for incompressible flows with moving boundaries.Communications in Computational Physics1552014, 12661290back to text
 5 articleBioinspired swimming simulations.Journal of Computational Physics3232016, 310  321
 6 articleModeling and simulation of fishlike swimming.Journal of Computational Physics23022011, 329  348
 7 articleAccurate Asymptotic Preserving Boundary Conditions for Kinetic Equations on Cartesian Grids.Journal of Scientific Computing2015, 34
 8 articleNumerical solution of the MongeKantorovich problem by density liftup continuation.ESAIM: Mathematical Modelling and Numerical Analysis4961577November 2015
 9 articleA Cartesian Scheme for Compressible Multimaterial Models in 3D.Journal of Computational Physics3132016, 121143back to text
 10 articleEnablers for highorder level set methods in fluid mechanics.International Journal for Numerical Methods in Fluids79December 2015, 654675
12.2 Publications of the year
International journals
 11 articleA projection‐based reduced‐order model for parametric quasi‐static nonlinear mechanics using an open‐source industrial code.International Journal for Numerical Methods in EngineeringNovember 2023HALDOIback to text
 12 articleRegistrationbased model reduction of parameterized PDEs with spatioparameter adaptivity.Journal of Computational Physics499February 2024, 112727HALDOI
 13 articleBalancing power production and coastal protection: A biobjective analysis of Wave Energy Converters.Renewable Energy220January 2024, 119702HALDOI
 14 articleQuantitative assessment of hippocampal network dynamics by combining Voltage Sensitive Dye Imaging and Optimal Transportation Theory.MathematicS In Action121September 2023, 117134HALDOI
 15 articleA oneshot overlapping Schwarz method for componentbased model reduction: application to nonlinear elasticity.Computer Methods in Applied Mechanics and Engineering404February 2023, 115786HALDOIback to text
 16 articleDatadriven wall models for Reynolds Averaged NavierStokes simulations.International Journal of Heat and Fluid Flow99January 2023, 109097HALDOI
 17 articleLocalized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment.SIAM Journal on Scientific Computing453June 2023, A1300A1331HALDOI
 18 articleA nonoverlapping optimizationbased domain decomposition approach to componentbased model reduction of incompressible flows.arXiv preprint arXiv:151792023HALDOI
 19 articleImplicit Relaxed All Mach Number Schemes for Gases and Compressible Materials.SIAM Journal on Scientific Computing455October 2023, A2632A2656HALDOI
 20 articleTopologically assisted optimization for rotor design.Physics of Fluids355May 2023HALDOI
International peerreviewed conferences
 21 inproceedingsMultiquery analysis of a PeWEC farm.Vol. 15 (2023): Proceedings of the European Wave and Tidal Energy Conference15Bilbao, SpainSeptember 2023HALDOI
 22 inproceedingsScalable Clustered Active Subspaces for Kriging in High Dimension.EUROGEN 2023  15th ECCOMAS Conference on Evolutionary and Deterministic Methods for Design, Optimization and ControlChania, Greece2023HALback to text
Conferences without proceedings
Edition (books, proceedings, special issue of a journal)
 24 proceedingsB.Beatrice BattistiT.Tobias BlickhanG.Guillaume EncheryV.Virginie EhrlacherD.Damiano LombardiO.Olga MulaWasserstein model reduction approach for parametrized flow problems in porous media.CEMRACS 2021  Data Assimilation and Reduced Modeling for High Dimensional Problems73EDP SciencesAugust 2023, 2847HALDOI
Reports & preprints
 25 miscProjectionbased model order reduction for prestressed concrete with an application to the standard section of a nuclear containment building.2024HALDOIback to text
 26 miscHigh order ADERIPDG methods for the unsteady advectiondiffusion equation.January 2024HAL
 27 miscA Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law.March 2023HAL
 28 miscA New Discontinuous Galerkin Formulation for the Boussinesq system with Naviertype boundary condition.May 2023HAL
 29 miscAn optimizationbased registration approach to geometry reduction.July 2023HAL
 30 miscCompositional maps for registration in complex geometries.2023HALDOI
Other scientific publications
 31 miscModel order reduction by convex displacement interpolation.October 2023HALDOIback to textback to textback to textback to textback to text
12.3 Cited publications
 32 articleA penalization method to take into account obstacles in a incompressible flow.Numerische Mathematik8141999, 497520back to text
 33 articleExact and approximate solutions of Riemann problems in nonlinear elasticity.Journal of Computational Physics228182009, 70467068back to text
 34 articleA Cartesian scheme for compressible multimaterial models in 3D.Journal of Computational Physics3132016, 121143URL: http://www.sciencedirect.com/science/article/pii/S0021999116000966DOIback to text
 35 articleAn experimental study of entrainment and transport in the turbulent near wake of a circular cylinder.Journal of fluid mechanics1361983, 321374back to text
 36 articleRegistrationbased model reduction of parameterized twodimensional conservation laws.Journal of Computational Physics4572022, 111068URL: https://www.sciencedirect.com/science/article/pii/S0021999122001309DOIback to text
 37 articleAutomatic Rigid Registration of Aortic Aneurysm Arterial System.March 2022HALback to text
 38 articleModelling wave dynamics of compressible elastic materials.Journal of Computational Physics22752008, 29412969back to text
 39 bookElements of continuum mechanics.Nauka Moscow1978back to text
 40 articleAn adaptive projectionbased model reduction method for nonlinear mechanics with internal variables: Application to thermohydromechanical systems.International Journal for Numerical Methods in Engineering123122022, 28942918URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6964DOIback to text
 41 articleMapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models.Journal of Computational Physics4712022, 111671URL: https://www.sciencedirect.com/science/article/pii/S0021999122007343DOIback to textback to textback to textback to text
 42 phdthesisConstruction d'une chaîne d'outils numériques pour la conception aérodynamique de pales d'éoliennes.Université de Bordeaux2014back to text
 43 articleA Conservative ThreeDimensional Eulerian Method for Coupled SolidFluid Shock Capturing.Journal of Computational Physics18312002, 2682back to text
 44 bookLevel Set Methods and Fast Marching Methods.Cambridge University Press, Cambridge, UK1999back to text
 45 articleA registration method for model order reduction: data compression and geometry reduction.SIAM Journal on Scientific Computing4222020, A997A1027back to text
 46 articleRegistrationbased model reduction in complex twodimensional geometries.submitted to Journal of Scientific Computing2021back to text
 47 articleSpacetime registrationbased model reduction of parameterized onedimensional hyperbolic PDEs.ESAIM: Mathematical Modelling and Numerical Analysis (accepted)2020back to textback to text