6.1.1 AGRIF

• Name:
  Adaptive Grid Refinement In Fortran
• Keyword:
  Mesh refinement
• Scientific Description:
  AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• Functional Description:
  AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• News of the Year:
  Within the framework of a European Copernicus contract, improvements have been made to the management of parallelization ( assignment of processors to computational grids).
• URL:
  https://­gitlab.­inria.­fr/­ldebreu/­agrif
• Publications:
  tel-01546328, hal-00387435
• Contact:
  Laurent Debreu
• Participant:
  Laurent Debreu

6.1.2 NEMOVAR

• Name:
  Variational data assimilation for NEMO
• Keywords:
  Oceanography, Data assimilation, Adjoint method, Optimal control
• Functional Description:
  NEMOVAR is a state-of-the-art multi-incremental variational data assimilation system with both 3D and 4D var capabilities, and which is designed to work with NEMO on the native ORCA grids. The background error covariance matrix is modelled using balance operators for the multivariate component and a diffusion operator for the univariate component. It can also be formulated as a linear combination of covariance models to take into account multiple correlation length scales associated with ocean variability on different scales. NEMOVAR has recently been enhanced with the addition of ensemble data assimilation and multi-grid assimilation capabilities. It is used operationnaly in both ECMWF and the Met Office (UK)
• Contact:
  Patrick Vidard
• Partners:
  CERFACS, ECMWF, Met Office

6.1.3 SWEET

• Name:
  Shallow Water Equation Environment for Tests, Awesome!
• Keywords:
  High-Performance Computing, Time integration methods
• Functional Description:

  SWEET supports periodic boundary conditions for - the bi-periodic plane (2D torus) - the sphere

  Space discretization - PLANE: Spectral methods based on Fourier space - PLANE: Finite differences - SPHERE: Spherical Harmonics

  Time discretization - Explicit RK - Implicit RK - Crank-Nicolson - Semi-Lagrangian - Parallel-in-time - Parareal - PFASST - Rational approximation of exponential Integrators (REXI) ...and many more time steppers...

  Special features - Graphical user interface - Fast Helmholtz solver in spectral space - Easy-to-code in C++ ...

  There’s support for various applications - Shallow-water equations on plane/sphere - Advection - Burgers’ ...

• URL:
  https://­sweet.­gitlabpages.­inria.­fr/­sweet-www/
• Contact:
  Martin Schreiber
• Partners:
  University of São Paulo, Technical University of Munich (TUM)

7.1.1 Numerical Schemes for Ocean Modeling

Participants: Eric Blayo, Laurent Debreu, Florian Lemarié, Gurvan Madec, Antoine Nasser, Pierre Lozano.

Beyond the hydrostatic assumption

With the increase of resolution, the hydrostatic assumption becomes less valid and the AIRSEA group also works on the development of non-hydrostatic ocean models. The treatment of non-hydrostatic incompressible flows leads to a 3D elliptic system for pressure that can be ill-conditioned, in particular with non geopotential vertical coordinates. That is why we favor the use of the non-hydrostatic compressible equations, that remove the need for a 3D resolution at the price of re-including acoustic waves. For that purposes a detailed analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean was carried out 47 in part in the PhD of E. Duval. The proposed numerical approach has been implemented in the CROCO ocean model and tested in various flow configurations 56, 62.

Most large scale ocean models are based on the so-called “primitive equations”, which use the hydrostatic and incompressibility assumptions. However, with the increase of resolution, a systematic use of the hydrostatic assumption becomes less valid. The French regional oceanic modeling system CROCO (Coastal and Regional Ocean COmmunity model, www.croco-ocean.org) developed these last years allows for the use of either the hydrostatic incompressible (HI) equations and the non-hydrostatic compressible (NHC) equations, the latter being much more computationally expensive. A natural idea is thus to limit the use of the NHC version to some particular regions of interest where the hydrostatic assumption is not relevant, and to nest such local NHC zooms within a larger model using the HI version. However such a coupling is quite delicate from a mathematical point of view, due to the different nature of hydrostatic and nonhydrostatic equations (where the vertical velocity is either a diagnostic or a prognostic variable). In his PhD, P. Lozano is working on the design of methods to couple local nonhydrostatic models to larger scale hydrostatic ones. He analyzed the constraints, in frequency space, associated with wave propagation between the hydrostatic and non-hydrostatic domains, and diagnosed their impact within a numerical model. This has been numerically validated in simplified configurations allowing the use of analytical solutions. Avenues are being explored to improve current coupling procedures, notably through the use of vertical mode decomposition and/or Perfectly Matched Layers techniques.

	$1/4^{\circ }$	$1/8^{\circ }$	$1/{12}^{\circ }$
$\sigma$
$\sigma$ penalized
AVISO

Show image description

Mean sea surface height in CROCO simulations at different resolutions for the standard case with terrain-following ($\sigma$) coordinates (top) and penalization (below). The third row shows the AVISO product for comparison

7.1.2 Coupling Methods for Oceanic and Atmospheric Models and representation of the Air-Sea Interface

Participants: Eric Blayo, Simon Clément, Florian Lemarié.

The Airsea team is involved in the modeling and algorithmic aspects of ocean-atmosphere (OA) coupling. We have been actively working on the analysis of such coupling both in terms of continuous and numerical formulations. Particular attention is paid to the inclusion of physical parameterizations in our theoretical framework. Our activities have led to practical implementations in state-of-the-art oceanic and Earth system models. Our focus during the last few years has been on the following topics:

1. Continuous and discrete analysis of Schwarz algorithms for OA coupling    Members of the Airsea team have been developing coupling approaches for several years, based on so-called Schwarz algorithms. Schwarz-like domain decomposition methods are very popular in mathematics, computational sciences and engineering notably for the implementation of coupling strategies. However, for complex applications (like in OA coupling) it is challenging to have an a priori knowledge of the convergence properties of such methods. Indeed coupled problems arising in Earth system modeling often exhibit sharp turbulent boundary layers whose parameterizations lead to peculiar transmission conditions and diffusion coefficients 67. In 11, the well-posedness of the non-linear coupling problem including parameterizations has been addressed and a detailed continuous and discrete analysis of the convergence properties of the Schwarz methods has been pursued to entangle the impact of the different parameters at play in such coupling problem. A general framework has been proposed to study the convergence properties at a (semi)-discrete level to allow a systematic comparison with the results obtained from the continuous problem. Such a framework allows the study of more complex coupling problems whose formulation is representative of the discretization used in realistic coupled models.
2. A simplified atmospheric boundary layer model for oceanic purposes    Part of our activities within the ongoing SHOM 19CP07 project is dedicated to the development of a simplified model of the marine atmospheric boundary layer (called ABL1d) of intermediate complexity between a bulk parameterization and a full three- dimensional atmospheric model and to its integration to the NEMO general circulation model 60. A constraint in the conception of such a simplified model is to allow an apt representation of the downward momentum mixing mechanism and partial re-energization 7 of the ocean by the atmosphere while keeping the computational efficiency and flexibility inherent to ocean-only modeling. Realistic applications of the coupled NEMO-ABL1d modeling system have been carried out and the methodology is being tested for integration into the operational forecasting system operated by Mercator-Ocean 3. Over the last year the approach has also been implemented in the CROCO ocean model. A focus has been to find adequate ways to fill some gaps in the 1D approach using multiple scales asymptotic techniques to cast the equations in terms of perturbations around an ambient state given by a large-scale datasets. Such simplified model called ABL3d leads to clear improvements over ABL1d for academic semi-idealized cases. The objective is now to extend the analysis to realistic cases in the framework of the ENMASSE project funded by the Copernicus Marine Environment Monitoring Service (CMEMS). In parallel, in the framework of the AIRSEA/Eviden collaboration, an objective is to design a surrogate via learning strategies of the response of the atmospheric boundary layer to anomalies in ocean surface temperatures and currents. A CIFRE thesis should be implemented on this subject during the year 2025.
3. Impact of the coupling formulation in a realistic context    A Schwarz-like iterative method has been applied in a state-of-the-art Earth-System model (IPSL-CM6) to evaluate the consequences of inaccuracies in the usual ad-hoc ocean-atmosphere coupling algorithms used in realistic models 63, 64. Numerical results obtained with an iterative process show large differences at sunrise and sunset compared to usual ad-hoc algorithms, thus showing that synchrony errors inherent to ad-hoc coupling methods can be large. However, such an iterative coupling method is too costly to be implemented operationally in climate models. In order to keep the computational cost almost constant w.r.t. the usual non iterative approach, the iterative algorithm would need to be provided with a first guess close to the optimum, so as to achieve quasi-convergence in a single iteration. We aim to obtain such an approximation of the optimal state by learning techniques (work of A. Monsimer as part of the programme national de recherche en intelligence artificielle - PNRIA). A learning network based on a test dataset restricted to a few fixed regions has been set up, and is indeed able to provide a first iteration of good quality. The remaining step is to scale up to a global scale, with a view to making the method operationally applicable to a climate model. As part of V. Schüller's thesis in collaboration with Lund University, a single-column version of the EC-Earth climate model is being used to further our study of coupling algorithms. The goal is to extend the analysis of 63 using a less complex model that remains representative of the parameterization schemes employed in 3D models. This single-column model has made it possible to focus on ocean-atmosphere coupling in the presence of sea ice. It was identified that the convergence of an iterative coupling in this context is compromised due to non-differentiabilities in the parameterization of albedo over sea-ice. This work is currently being finalized, and a publication is in preparation.

These topics are addressed through strong collaborations between the applied mathematicians and the climate and operational community (Meteo-France, Ifremer, SHOM, Mercator-Ocean, LMD, and LOCEAN). Airsea team members play a major role in the structuration of a multi-disciplinary scientific community working on ocean-atmosphere coupling spanning a broad range from mathematical theory to practical implementations in climate and operational models.

7.1.3 Physics-Dynamics coupling: Consistent subgrid-scale modeling

Participants: Eric Blayo, Simon Clément, Florian Lemarié, Manolis Perrot.

For approximately 5 years, the AIRSEA team has started to work on new topics around physics-dynamics coupling 55. Schematically, numerical models consist of two blocks generally identified as “physics” and “dynamics” which are often developed separately. The “Physics” represents unresolved or under-resolved processes with typical scales below model resolution while the “dynamics” corresponds to a discrete representation in space and time of resolved processes. Unresolved processes cannot be ignored because they directly influence the resolved part of the flow since energy is continuously transferred between scales. The interplay between resolved and unresolved scales is a large, incomplete and complex topic for which there is still much to do within the Earth system modeling community 59. During the last year we worked on the following topics :

1. Representation of penetrative convection in oceanic models    Accounting for the mean effect of subgrid scale intermittent coherent structures like convective plumes is very challenging. Currently this is done very crudely in ocean models (vertical diffusion is locally increased to “mix'’ unstable density profiles). A difficulty is that in convective conditions, turbulent fluxes are dominated by processes unrelated to local gradients, thus invalidating the usual downgradient (a.k.a. eddy-diffusion) approach. In the framework of the PhD of M. Perrot, a first step is to study the derivation of mass-flux convection schemes arising from a multi-fluid decomposition to extend them specifically to the oceanic context. This extension is done under certain “consistency" constraints: energetic considerations and scale-awareness of the resulting model 35. Reference LES simulations have been developed to guide the formulation of unknown/uncertain free parameters (coefficients or functions) in the proposed extended mass-flux scheme 36. The Bayesian calibration of such free parameters will be undertaken.
2. Partially Lagrangian implementation of location uncertainty    Recent oceanic parameterizations "under Location Uncertainty" are based on the hypothesis that the small-scale processes are uncorrelated in time. The implementation of such parameterizations can be done in a Lagrangian manner, with rapidly moving grid points. The possibility of keeping the grid close to its original disposition was studied by S. Clement to understand how the time correlation induced by this constraint can be compensated by an Eulerian term. In particular he showed that the easy-to-implement Stochastic Grid Perturbation method 61 can be interpreted in the framework of Location Uncertainty 24.

Those topics are addressed through collaborations with the climate and operational community (Meteo-France, SHOM, Mercator-Ocean, and IGE). Two projects are currently funded, one on the energetically consistent discretization aspect (SHOM 19CP07, 2020-2025, PI: F. Lemarié) and one on the convection parameterization (Institut des Mathématiques pour la Planète Terre, 2021-2024, PIs: F. Lemarié and G. Madec). Furthermore, the Airsea team is involved in the PLUME ANR project. One of the objectives of this project is to use LES numerical simulations and laboratory experiments of deep convection to calibrate and evaluate physical parameterizations like the one developed in 36. Furthermore, the Airsea team has been involved in organizing a workshop, funded by LEFE, on the "representation of fine oceanic scales in Numerical Simulations" which took place in Brest in Oct. 2024. The workshop was at the interface of geophysical fluid dynamics and numerical techniques, as the two are deeply interconnected. The workshop aimed to collectively address the scientific challenges and future stakes related to the following topics, which are at the crossroads of geophysical fluid dynamics and numerical techniques: review of parameterizations widely used in our fields, continuum between resolved and subgrid scales in ocean models, exploitation of the model hierarchy operating at varying spatial resolutions for the calibration of deterministic or stochastic parameterizations, and techniques for parameter calibration and quantification of uncertainties in parameterizations.

7.2.1 Model Reduction

Participants: Clémentine Prieur, Katarina Radišić, Romain Verdière, Arthur Vidard, Olivier Zahm.

When numerical models are too costly to evaluate, it is common to address the task of uncertainty quantification using an approximate model, which is faster to compute. However, constructing such a reduced model (or surrogate) is challenging due to the high number of variables involved. It is therefore crucial to identify the input variables that are most important for building the reduced model.

In 68, we propose a nonlinear dimensionality reduction method that leverages gradient evaluations of the model. Similar to prior work 48, the objective is to align the Jacobian of the feature map (a nonlinear function that extracts the key components of the parameters) with the model's gradients. Our main contribution is to use feature maps defined as the first components of a diffeomorphism from ${ℝ}^d$ to ${ℝ}^d$, parameterized by a Coupling Flows neural network. This architecture preserves essential properties of the feature map, notably ensuring that its level sets remain simply connected. In addition, we propose a dimension augmentation trick to increase the approximation power of feature detection. A generalization to vector-valued functions demonstrate that our methodology directly applies to learning autoencoders, showing the versatility of our proposed framework.

Complementarily in Billaud-Friess et al. 1 we introduced a probabilistic Reduced Basis Method (RBM) for the approximation of a family of parameter-dependent functions, that leverages a probabilistic greedy algorithm with Monte Carlo estimates. This method incorporates an error indicator expressed as the expectation of a parameter-dependent random variable, enabling high-probability weak greedy algorithm performance. Designed for noisy, parameter-dependent evaluations, the approach finds practical application in approximating solution manifolds of parameterized PDEs, interpreted probabilistically through the Feynman-Kac formula.

On a related topic, in her PhD work, Katarina Radišić conducted an in-depth investigation into the use of stochastic polynomial chaos expansion, where the coefficients of the polynomial basis are themselves treated as random variables. This approach allows for an efficient representation of external uncertainties while retaining the computational efficiency of a surrogate emulator. Such a framework proves particularly advantageous for problems involving complex systems with significant variability in external conditions. This methodology was adaptated to a hydrological and pesticide transfer model, where the primary external uncertainty arose from variability in rainfall. By incorporating this uncertainty directly into the stochastic framework, the model achieved a flexible representation of system behavior under varying environmental conditions. This was in turn used extensively in the context of sensitivity analysis and for robust parameter estimation, see (7.3.1, 7.3.4).

7.2.2 Multifidelity

Participants: Elise Arnaud, Hélène Hénon, Angélique Saillet, Martin Schreiber, Arthur Vidard, Olivier Zahm, Benjamin Zanger.

Multifidelity methods seek to balance the computational load across a hierarchy of models with varying accuracy and evaluation cost, using lower-fidelity models for inexpensive approximations and higher-fidelity ones only when necessary. By integrating information across fidelities, it ensures better performance for complex tasks. The efficiency of such an approach, however, relies on our ability to decide on how to allocate resources on the different level of accuracy in order to reduce overall computation while maintaining accuracy.

1. Sampling

   In 43, we adapt the concept of multifidelity to sample from complex densities, such as posterior densities in Bayesian inference. The idea is to introduce a sequence of densities with intermediate complexity, ranging from a simple density to sample from (= prior) to the target density (= posterior). We then learn each density sequentially by preconditioning the n-th step with the transport map that couples a reference measure (e.g., Gaussian) with the (n-1)-th density. This reduces the complexity of each step, significantly improving numerical performance compared to a direct approach. The paper 43 also addresses the choice of intermediate densities (ie, the multifidelity) based on the problem at hand: tempering/annealing for Bayesian inference tasks and diffusion-based models for densities that are accessible only from data.

2. Variational data assimilation

   Incremental Variational Data Assimilation addresses the non-linear least-square optimization challenges inherent in variational data assimilation by minimizing a sequence of linear least-squares cost functions iteratively. However, due to the high dimensionality and ill-conditioning of the associated problems, the computational burden can become prohibitive. To address these challenges, we propose two approaches leveraging multifidelity methods and machine learning to improve efficiency and reduce computational costs.

   The first approach, explored in the context of Hélène Hénon's PhD research, investigates the application of multifidelity strategies to tackle the linear problem. Two specific strategies have been proposed. The first strategy employs inexact conjugate gradient methods, allowing for convergence results while respecting a controlled inaccuracy budget, which directly reduces computational time. The second strategy uses local multifidelity corrections through trust-region optimization, enabling dynamic adjustments to fidelity levels based on the local problem characteristics, thereby improving the overall efficiency of the iterative process.

   The second approach addresses the challenge of performing repeated inversions of large and potentially ill-conditioned matrices, which is a bottleneck in the optimization process. To improve the convergence rate and alleviate the computational burden, we propose utilizing Deep Neural Networks to construct a preconditioner. This preconditioner is trained on properties derived from the singular value decomposition of the matrices, ensuring it effectively mitigates the effects of ill-conditioning. To further optimize resource utilization, the training dataset is designed to be constructed dynamically during the optimization process, thereby reducing storage requirements. This work is detailed in a preprint 41.

3. Exploration of climate scenarios

   Numerical models are important tools for predicting climate change and helping policy-makers to make decisions (e.g. in terms of protecting marine areas, land use or defining fishing quotas). The huge complexity of models and the generally very high cost of numerical simulations make an exhaustive exploration of the parameter space, corresponding to all possible scenarios and all the model's internal options, completely illusory. The idea is therefore to use statistical tools for the design of experiments. These tools enable us the parameter combinations that provide the most information on a given quantity of interest (QoI - e.g. an ecosystem health indicator) calculated from the simulation carried out. The design of experiments also has the advantage of being able to be built adaptively, in order to take into account the results of pre-existing simulations, performed with various models, under various scenarios. In Angelique Saillet's PhD, we aim at developing methodologies to address these issues, exploiting theoretical tools such as sequential design of experiments, enrichment strategies, and multi-fidelity Gaussian process regression. This work is carried out in the context of a marine biogeochemistry model, in collaboration with M. Baklouti (MIO Marseille). A sensitivity analysis has been performed on a 1D (vertical) version of the model, in order to identify the parameters that are most influential for certain quantities of interest (QoI). This enables the construction of meta-models for these QoI, thanks to the use of Gaussian processes. The next step will be to investigate how the use of additional “low-fidelity’' simulations performed with one or several degraded versions of the model can improve these metamodels.

7.3.1 Sensitivity Analysis

Participants: Alexis Anagostakis, Elise Arnaud, Qiao Chen, Clémentine Prieur, Katarina Radišić, Arthur Vidard, Ri Wang, Olivier Zahm.

Sensitivity analysis is a crucial step in uncertainty quantification as it helps identifying which input variables most influence the variability in a model's output. This understanding guides model simplification, parameter prioritization, and robust decision-making. Our research results this year can be organized around three main axes :

1. GSA for non-classical problem settings

   The classical framework for GSA assumes that the model is a deterministic function of an input random vector with independent components. However, real-world applications often deviate from this assumption.

   • In 2, we tackled the challenge of estimating total effects under constrained feature settings. Our approach addressed feature correlations and non-Cartesian domains through experimental designs and computational techniques.
   • In 42 we introduced a Quantile-Oriented Sensitivity Analysis (QOSA) framework, leveraging random forests with pinball loss to address biases and improve accuracy in high-dimensional input spaces.
   • Traditional GSA often neglects natural variability in forcing conditions, limiting result validity. In 37, we treat Sobol’ indices as random variables influenced by forcing variability and estimate them efficiently using stochastic polynomial chaos expansions. Applying this to a hydrological model, we found parameter rankings vary with forcing, and proposed an aggregated sensitivity index to enhance GSA robustness and decision reliability.
   • In 26, we introduced novel estimators for Sobol’ indices that require only a single input/output samples. Numerical results demonstrate that these estimators enhance computational efficiency while maintaining robustness and asymptotic efficiency.

2. Gradient-based methods

   When model gradients are available, gradient-based sensitivity methods offer a convenient and efficient alternative to traditional approaches. Over the past year, we have proposed several improvement of such gradient-based sensitivity analysis:

   • Coupled input-output dimension reduction for vector valued model 23. Unlike conventional approaches that address input or output reduction separately, our coupled approach selects the most relevant components for tasks like sensor placement and sensitivity analysis. By optimizing gradient-based bounds, we efficiently identify key inputs and outputs, avoiding costly combinatorial optimization.
   • Certified coordinate selection method for Bayesian inverse problem with heavy tail prior (Laplace), with application in imaging application 27, 54. We reduce the parameter to a small number of relevant coordinates contributing most to the prior-to-posterior update, identified via a gradient-based diagnostic. For linear forward models with Gaussian likelihoods, tractable methods estimate the diagnostic before solving the problem, enabling efficient posterior inference. Applications include 1D signal deblurring and high-dimensional 2D super-resolution, with improved sampling using specialized MCMC methods.

3. GSA for epidemic models

   In 5, we applied global sensitivity analysis to a SARS-CoV-2 epidemic model based on continuous-time Markov chains. This work quantified uncertainty arising from both parameter values and intrinsic randomness, while exploring how different simulation algorithms impact sensitivity results. Building on these efforts, 30 extended the Sellke construction to non-Markovian models, enabling sensitivity analyses for more complex epidemic frameworks like the SEI1I2RS model. This generalisation expanded sensitivity methods to include both stochastic and epistemic uncertainties across a wide range of compartmental models.

7.3.2 Bayesian inversion

Participants: Adama Barry, Clément Duhamel, Clémentine Prieur.

Bayesian inverse problems become challenging when computational models are expensive, as the repeated evaluations required for inference (e.g., in Markov Chain Monte Carlo) become infeasible. Additionally, complex priors, such as those with heavy tails or multimodal distributions, complicate sampling and convergence, making efficient exploration of the posterior space significantly harder.

In 27, we study Bayesian inverse problems with Gaussian likelihood, linear forward models, and priors represented as Gaussian mixtures. The posterior also forms a Gaussian mixture, and we derive a closed-form expression for the posterior mixing density. To efficiently sample from this posterior, we propose a two-step method using dimension-reduced approximations for the mixing density, which maintain accuracy while ensuring low correlation in the generated samples.

In 19 we propose a hybrid approach, using a Gaussian process emulator to optimize physical experimental designs and sequentially refining numerical experiments to improve calibration. New criteria inspired by the Sequential Uncertainty Reduction (SUR) paradigm for experiment selection and performance comparisons demonstrated effectiveness on test cases, including a harmonic oscillator calibration.

For practical applications, the definition of the space the set of feasible model input values is generally not trivial. During Clément Duhamel's PhD, we have focused on the estimation of a feasible set defined by an inequality constraint on the output of a time-consuming black-box simulator. More precisely, we have proposed in 52 a new criterion for bayesian active learning for the estimation of such a feasible set, for a black-box simulator with scalar outputs. In an ongoing work (to be submitted soon), we extend this work to the framework of vector-valued black-box emulators.

7.3.3 Sampling algorithms

Participants: Elise Arnaud, Qiao Chen, Rafael Flock, Martin Schreiber, Olivier Zahm, Benjamin Zanger.

Sampling from high-dimensional distributions that are multi-modal and/or heavy-tailed poses significant challenges across various fields. This is particularly true in large-scale Bayesian inference with sparsity-inducing priors, but also, for example, in molecular dynamics, where the Boltzmann distribution of a molecular system is highly multimodal, each of the mode corresponding to a distinct physical conformation. Conventional sampling methods such as Markov Chain Monte Carlo (MCMC) face difficulties in accurately exploring the entire landscape (modes, tails, etc) of the target distribution, resulting in poor numerical performances. We have made diverse contributions which aim at addressing these challenges, focusing on a range of applications including imaging, epidemiology, and also on providing proof-of-concepts for certain advanced pioneering algorithms. These contributions involve the development of

• a.
  dimension reduction techniques 6, 27, 23, 54
• b.
  transport maps methods 43
• c.
  preconditioners for stochastic differential equations (SDE) in order to enhance the convergence properties of sampling algorithms 25.

7.3.4 Robust inversion

Participants: Elise Arnaud, Exaucé Luweh Adjim Ngarti, Katarina Radišić, Arthur Vidard.

Estimating key parameters in numerical models is a crucial aspect in numerical simulation, particularly when these parameters are not directly observable. Traditional estimation methods infer parameters indirectly from their effects on observable variables, introducing inherent uncertainties. In addition to the parameters to be estimated, numerical models often include uncertain and uncontrollable nuisance parameters, which can further complicate the estimation process.

In Exaucé Ngarti’s PhD research, we investigate extending variational inference to account for the presence of nuisance parameters. Ignoring the stochastic nature of these nuisance parameters can lead to suboptimal parameter estimation due to error compensation effects. To address this, we model nuisance parameters as random variables, redefining the numerical model itself as a random variable. This problem is formulated within a Bayesian framework, where the goal is to estimate the posterior distribution by minimizing the Kullback-Leibler divergence over a family of parameterized distributions. To increase the flexibility of this approach, we integrate generative neural networks, such as normalizing flows, to enhance the expressiveness of the posterior approximation. These methods are applied to the shallow water model to estimate the friction coefficient, a critical parameter in coastal modeling that characterizes the seabed's roughness. In this context, the nuisance parameters represent boundary forcing effects driven by tidal frequencies and amplitudes.

In Katarina Radišić’s PhD research, we explore an alternative approach based on optimal control. Here, the parameter estimation problem is addressed by minimising an objective function. When nuisance parameters are present, the objective function becomes a random variable, adding a layer of complexity. To efficiently handle this uncertainty, we employ stochastic polynomial chaos expansion as a surrogate for the "random" objective function. This technique enables effective exploration of the uncertain parameter space and facilitates the computation of robust parameter estimates. The methodology has been successfully applied to a hydrology and pesticide transfer model, demonstrating its feasibility. A publication detailing this work is currently in preparation.

7.4.1 Dynamic compute-resource utilization

Participants: Martin Schreiber.

The way how applications are executed on supercomputers still follows a traditional static resource allocation pattern: Computing resources are allocated at the start of a job which executes the application and are only released at the end of the job's runtime. This still follows the way of running jobs since decades where a dynamic resource allocation over the application's runtime would lead to several benefits: higher utilization of the computing resources, ad-hoc allocation of AI accelerator cards, less energy consumption, faster response for interactive jobs, improved data locality and I/O over the full runtime, support of urgent computing without necessarily killing running jobs, etc. Various attempts have been conducted under different terminologies used such as “evolving” jobs (application-driven dynamic resource changes) and “malleability” (system-driven dynamic resource changes) where we see a hybridization of them required for reaching optimal results.

We currently investigate possibilities to extend the MPI parallel programming model (which is the de-facto standard in HPC) and also models beyond MPI with such interfaces. As part of that, we participate in regular MPI Session working group meetings where certain effort has been done to investigate such interfaces. Based on previous work 53, 58, 57 we finally wrote the paper “Design Principles of Dynamic Resource Management for High-Performance Parallel Programming Models” 29 explaining the basic requirements and rationality of what a generic dynamic resource APIs would need to support. Together with other EuroHPC projects, we also worked on a state-of-the-art paper on “Malleability in Modern HPC Systems: Current Experiences, Challenges, and Future Opportunities”1.

External collaborators: Dominik Huber (TUM, DataMOVE), Pierre-François Dutot (DataMOVE), Olivier Richard (DataMOVE), Howard Pritchard (LANL), Martin Schulz (TUM)

7.4.2 Hardware-aware numerics

Participants: Hugo Brunie, Laurent Debreu, Julien Remy, Martin Schreiber.

We made further progress toward a Domain-Specific Language (DSL) for the NEMO and CROCO ocean simulation model to close the increasing gap between the numerics and HPC with a separation of concerns. Such a DSL would allow applied mathematicians to express their model equations in a high-level language and HPC experts to develop tools to automatically transform this into highly performing code on the target programming model and corresponding architecture. For our DSL, we work with PSyclone, a code generation and transformation system for Fortran-based developments, and we would like to gratefully acknowledge various developments (partly unpublished) of PSyclone developers that accelerated our success.

The Poseidon project has been kicked off, working on the vision to push the performance of the above-mentioned ocean models to the HPC limit with in-depth optimizations that can't be done with currently existing compilers and to simplify the development of highly performing code for model developers.

The underlying idea is to uplift the fluid dynamics equation solver to a DSL-like intermediate representation (IR). This IR is based on a hypergraph with nodes representing computations and (hyper)edges the data flow. The strong formalism of the IR representation forms the foundation for performing the required HPC optimization, and all transformations are exclusively done in this representation. Poseidon supports writing back code to the original ocean model; hence, it doesn't require using a different development which would require disruptive changes.

Based on the extracted barotropic solver of the CROCO model, our first HPC results are to perform a fully automatic kernel fusion. This fusion already led to a substantial reduction of memory access, leading to speedups of up to 2.9.

Further work has been conducted in collaboration with Anna Mittermair & Martin Schulz (Technical University of Munich) on optimizing the communication for distributed memory systems. Former work (Master's thesis by Anna Mittermair (See 2023 MA anna mittermair.pdf) showed that obsolete communications can be detected, but that automatically inferring the required communication (as the fundament of optimizing for it) with existing means of Psyclone is hardly feasible in a reliable way. Based on Poseidon and the very formal hypergraph IR, we can already automatically inject nodes into the hypergraph to perform automatic MPI communication. The current work-in-progress is on automatically inferring optimal communication, realizing its backend to write back code to an ocean model, and working on further enhancements.

We also investigate data assimilation requiring the computation of adjoints of time steps with automatic differentiation. Realizing this by hand is a non-trivial process and requires maintenance by an expert every time the numerics are updated. Also, using automatic tools results in functionally correct differentiated code but generates code lacking various potentials for optimization. Based on the previous experience with PSyclone for automatically generating code for adjoints as a proof-of-concept for simple ODE examples (psyclone-autodiff.readthedocs.io), we can now apply a first prototype of the tangent computation based on the Poseidon hypergraph IR. The adjoint is currently work-in-progress.

Finally, explaining HPC optimization (e.g., kernel-fusion) to those unfamiliar with standard HPC optimizations is often challenging. To also reach out to such non-HPC experts, e.g., as part of open days, we are currently developing a web browser visualization in collaboration with TUM to explore and dynamically change the hypergraph (e.g., by applying hypergraph operations such as kernel fusion), including visualization of its performance change.

External collaborators: Anna Mittermair (TUM), Rupert Ford $†$ (STFC), Andrew Porter (STFC), Sergi Siso (STFC), Jörg Heinrichs (ABOM)

7.4.3 New time-integration methods

Participants: Martin Schreiber.

We investigate new time-integration methods by considering HPC requirements, targeting a better wallclock time vs.  error ratio. These numerical methods include exponential, semi-Lagrangian, and parallel-in-time integration methods.

We explored and extended semi-Lagrangian exponential methods, which integrate stiff linear terms with exponential time integration and handle nonlinear advection using a semi-Lagrangian approach. These techniques are relevant for partial differential equations found in atmospheric models. A truncation error analysis reveals that existing methods are limited to first-order accuracy due to linear term discretization. To address this, we develop a second-order scheme. Stability comparisons between various Eulerian and semi-Lagrangian exponential methods and a widely used semi-Lagrangian semi-implicit method are conducted. Numerical tests on shallow-water equations confirm the proposed method's improved stability and accuracy, albeit with higher computational costs. However, its stability and cost are comparable to the semi-implicit method, making it a competitive option for atmospheric modeling 2. This forms an extremely important part for future work on parallel-in-time methods.

Spectral Deferred Correction (SDC) methods show promise for atmospheric modeling in parallel computing environments. This study focuses on applying ETDSDC, a novel SDC family with strong stability and efficiency, to weather simulation. Using the SWEET academic HPC solver, ETDSDC is tested on Dahlquist’s equation and the Shallow Water Equations with the Williamson and Galewsky cases. Our findings show that ETDSDC demonstrates superior convergence rates, including super-convergence, outperforming methods like LRK, ETDRK, and IMEXSDC, particularly in higher-order formulations. However, stability challenges arise with high local gradients and spectral discontinuities. Additionally, the Lawson Runge-Kutta (LRK) scheme is unexpectedly the most runtime-efficient one 3.

External collaborators: Pedro S. Peixoto (USP), João C. Steinstraesser (USP), Elizaveta Boriskova (TUM)

9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program

Crocodiles (team.inria.fr/crocodiles/):

Optimization of PDE solvers is one of the big challenges in High-Performance Computing (HPC). This requires not only skills and a deeper understanding of HPC from all the hardware and software layers but also research on software solutions that are sustainable and accepted by the developers and users of these solvers.

This associate team brings together members of ANL and the Inria Airsea team who are both currently working on the HPC modernization of models under the aforementioned constraints. This allows us to share, on the one hand, our experience and plans with the model developments. On the other hand, we can strongly benefit from the experience of all the current developments, which share many similarities.

We identified parts of mutual interests such as sharing the modularization concepts of software developed at ANL and the code analysis (based on Psyclone and also Poseidon) developed by the Airsea team. Future work will be investigating the code analysis with Psyclone on their Flash-X code.

9.1.2 STIC/MATH/CLIMAT AmSud projects

9.1.3 Participation in other International Programs

9.2.1 Visits of international scientists

9.3.1 Other european programs/initiatives

• Program: CMEMS
  • Project acronym:
    ENMASSE
  • Project title:
    Enhancing Nemo for Marine Applications and Services
  • Coordinator:
    F. Lemarié
  • Duration:
    Dec. 2024 - Dec. 2027.
  • Other partners:
    CMCC (Italy), Sorbonne Université, MetOffice (UK), National Oceanography Center (UK), STFC Hartree Centre (UK), Datlas (FR).
  • Abstract:
    The Enhancing NEMO for Marine Applications and Services (ENMASSE) project represents a pivotal initiative aimed at advancing the capabilities of the NEMO (Nucleus for European Modelling of the Ocean) modelling platform. This enhancement is designed to address specific scientific and operational requirements set by the Copernicus Marine Service (CMS) program for the development and delivery of more precise and sophisticated ocean modelling products. These products are intended to support a wide range of applications, including marine safety, climate prediction, and ecosystem monitoring, ultimately contributing to informed decision-making and sustainable ocean management.
• Program: C3S2
  • Project acronym:
    ERGO2
  • Project title:
    Advancing ocean data assimilation methodology for climate applications
  • Duration:
    August 2022 - July 2025
  • Coordinator:
    Arthur Vidard
  • Other partners:
    Cerfacs (France), CNR (Italy)
  • Abstract:
    The scope of this contract is to improve ocean data assimilation capabilities at ECMWF, used in both initialization of seasonal forecasts and generation of coupled Earth System reanalyses. In particular it shall focus on i) improving ensemble capabilities in NEMO and NEMOVAR and the use of their information to represent background error statistics; ii) extend NEMOVAR capabilities to allow for multiple resolution in multi-incremental 3D-Var; iii) make better use of ocean surface observations. It shall also involve performing scout experiments and providing relevant diagnostics to evaluate the benefit coming from the proposed developments.

9.4.1 ANR

• A 4-year contract: ANR MOTIONS (Multiscale Oceanic simulaTIONS based on mesh refinement strategies with local adaptation of dynamics and physics).
  • PI:
    F. Lemarié
  • Duration:
    Jan. 2024 - Dec. 2027.
  • Other partners:
    • Laboratoire d’Aérologie, UMR 5560 (LAERO),
    • Service Hydrographique et Océanographique de la Marine (SHOM),
    • Institut Camille Jordan,
    • UMR5208 (ICJ),
    • Laboratoire d’Etudes en Géophysique et Océanographie Spatiales,
    • UMR5566 (LEGOS).
  • Abstract:
    The MOTIONS project aims at delivering robust and efficient numerical algorithms allowing an innovative multiscale modeling strategy based on block-structured mesh refinement with local adaptation of model equations, numerics and physics in selected areas of interest. The target application to evaluate numerical developments is the simulation of important fine-scale non-hydrostatic processes and their feedback to larger scales within the Mediterranean / North-East Atlantic dynamical continuum.
• A 4-year contract: ANR PLUME (Observation and Parameterization of Oceanic Convection).
  • PI:
    B. Deremble (CNRS), Inria PI: F. Lemarié.
  • Objectives:
    1. build a consistent database of convective events (both in the lab and with a numerical model) in order to calibrate free parameters of parameterizations of deep convection.
    2. characterize the structure of the thermal plumes in a well defined parameter space that characterizes the rotating/non rotating state and forced vs free convection
    3. use a data driven approach to formulate a model of convection without any preconceived bias about the mathematical formulation.
• Several team members also participate to PEPR NUMPEX and MathsVives

9.4.2 Inria Challenge

• Sea Uncertainty Representation and Forecast (SURF),
• Coordinator: Airsea (A. Vidard),
• Partenaires Inria: Ange, Cardamom, Fluminance, Lemon, Mingus, Defi
• Partenaires extérieurs: BRGM, Ifremer, SHOM

9.4.3 Other Initiatives

• E. Blayo is co-advising the PhD thesis of Valentin Bellemin-Laponnaz with IGE Lab, in the framework of the NASA-CNES working group on the SWOT satellite.
• A 3-year contract (started in Sept 2021) funded by the Institut des Mathématiques pour la Planète Terre (IMPT) on the topic "Modélisation cohérente des échelles sous-maille pour les modèles océaniques de climat" (PI: F. Lemarié).

10.1.1 Scientific events: organisation

The Airsea team organized the 3rd SDC days in Grenoble: sdc2024.sciencesconf.org/

The age of exascale computers brought new challenges to computational science, emphasizing the efficient use of modern high-performance computing systems. The shift to massive parallelism posed significant difficulties in designing numerical algorithms. This demand was particularly pressing in fields requiring simulations of systems evolving from initial conditions. Spectral Deferred Correction (SDC) methods, an iterative solver framework, provided higher-order temporal integrators for ODEs and PDEs with various options for parallelization in time. The meeting aimed to promote exchange on advanced time integrators, covering analytical and numerical analyses, as well as software and implementation aspects.

10.1.2 Scientific events: selection

10.1.3 Journal

10.1.4 Invited talks

• E. Blayo was the invited speaker of the first Plugin seminar at Inria Grenoble, March, 19, 2024.
• M.Schreiber was the invited speaker at Geneve University: Breaking through the barrier of time integration for climate and weather simulations, Dec. 2024
• M.Schreiber was the invited speaker of the HPC Seminar @ Bordeaux: Perspectives of weather and climate simulations on next-generation HPC systems, Bordeaux (virtual), May 2024
• M.Schreiber was the invited speaker of the NHR PerfLab Seminar: Breaking through the barrier of time integration for climate and weather simulations, Erlangen, Mar. 2024

10.1.5 Leadership within the scientific community

• F. Lemarié is member of the international CLIVAR Ocean Model Development Panel since Jan. 2024. CLIVAR (Climate and Ocean: Variability, Predictability, and Change) is a core project of the World Climate Research Program (WCRP).
• F. Lemarié is member of the scientific board of the GDR "Défis théorique pour les sciences du climat" (since Dec. 2024)
• C. Prieur is the ongoing president of SAMO group, international research group on sensitivity analysis.

10.1.6 Scientific expertise

• E. Blayo is a member of the scientific committee of IMPT (Institut Mathématique pour la Planète Terre)
• E. Blayo is a member of the scientific committee of the Labex Persyval-3
• F. Lemarié is the co-leader with Sybille Téchené (CNRS) and Mike Bell (UK Met Office) of the NEMO (www.nemo-ocean.eu) Working Group on numerical kernel development.
• F. Lemarié is a member of the CROCO (www.croco-ocean.org) scientific committee in charge of the "numerical methods" topic.
• Martin Schreiber is a member of the MPI Forum (representing the University Grenoble Alpes) and in particular active in the MPI Session workgroup.
• Martin Schreiber is a member of the OpenMP ARB (representing Inria).
• Clémentine Prieur is advisor to the scientific council of IFPEN.

10.1.7 Research administration

• E. Blayo is a deputy director of the Jean Kuntzmann Lab.
• Clémentine Prieur is Vice President of the french society of statistics (SFdS) since July 2024.
• Clémentine Prieur is currently a member of the Executive and Scientific Committees of the RT Quantification d’Incertitudes (RT2172 funded by INSMI @ CNRS) which she chaired during the period 2010-2017.
• Clémentine Prieur is currently a member of the Scientific Committee of the RT Terre et Energies (RT2166 funded by INSMI @ CNRS).
• Clémentine Prieur is local correspondent in Grenoble for the Mathematical Society of France (SMF).
• Clémentine Prieur was a member of the MSTIC pole council of UGA(nov. 2020-oct. 2024).
• Clémentine Prieur is responsible for the applied math specialty for doctoral school MSTII edmstii.univ-grenoble-alpes.fr
• E. Arnaud is in charge of the parity diversity commission at Jean Kuntzmann Lab
• F. Lemarié is member of the local Inria ”comité des emplois scientifiques” (CES), responsible for evaluating delegation requests and awarding Inria postdoc fellowships (since Sept 2019).
• F. Lemarié is the Inria local scientific correspondent for national calls for projects (work in coordination with Inria contract managers to identify national project calls and the teams that may be suited to respond to these calls. As part of this mission, I provide support to (1) analyze the objectives of project calls to assess their relevance. (2) track trends and innovations in the relevant sector). (since July 2020)

10.2.1 Teaching

• Licence: E. Arnaud, Mathematics for engineers, 50h, L2, UGA, France
• Licence: E. Arnaud, Statistics, 20h, L2, UGA, France
• Licence: E. Blayo, analysis and algebra, 107h, L1, University Grenoble Alpes, France
• Licence: C. Kazantsev, Mathématiques approfondies pour l'ingénieur, 36h, L2, UGA, France
• Licence: C. Kazantsev, Mathématiques pour les sciences de l'ingénieur, 36h, L2, UGA, France
• Licence: Martin Schreiber, Advanced Analysis & Algebra, L1, 69h, UGA, France
• Master: E. Arnaud, Statistics, 30h, M1, UGA, France
• Master: E. Arnaud, Supervision of student in apprenticeship, 30h, M2, UGA, France
• Master: E. Blayo, Partial Differential Equations, 37h, M1, University Grenoble Alpes, France
• Master: E. Blayo, Optimal control of PDEs, 17h, M2, University Grenoble Alpes, France
• Master: Martin Schreiber, High-Performance Computing, M1, 31.1h, UGA, France
• Master: Martin Schreiber, Parallel Algorithms and Programming, M1, 11.25h, UGA, France
• Master: Martin Schreiber, Object oriented programming with C++, M1, 18h, UGA, France
• Master: Martin Schreiber, Partial differential equations, M1, 34.5h, UGA, France
• E-learning: E. Arnaud is in charge of the pedagogic platform math@uga: implementation of a collaborative moodle platform to share pedagogical resources within teachers and towards students.
• E. Blayo is in charge of the Ecole des Mathématiques Appliquées: organization and coordination of pedagogical and administrative aspects related to teaching for the applied maths department.

10.2.2 Supervision

• PhD in progress: Pierre Lozano, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2022, E. Blayo and L. Debreu
• PhD in progress: Manolis Perrot, Consistent subgrid scale modeling for oceanic climate models. October 2021, E. Blayo and F. Lemarié
• PhD in progress: Gabriel Derrida, Design of flexible and numerically-sound generalised vertical coordinates with vertical ALE (V-ALE) algorithm for operational ocean forecasting. October 2023, L. Debreu and F. Lemarié.
• PhD in progress: Angélique Saillet, Design of experiments, climate scenarios and ocean simulation, Octobre 2023, Eric Blayo and Élise Arnaud.
• PhD in progress: Exaucé Luweh Adjim Ngarti, deep learning for inverse problem in geophysics, Université Grenoble-Alpes Avril 2023, E. Arnaud, L. Nicoletti (Atos) and A. Vidard.
• PhD in progress: Julien Remy, “HPC Automatic differentiation for ocean models, since Octobre 2024, M. Schreiber and A. Vidard
• PhD in progress: Benjamin Zanger, Compositional surrogates for reduced order modeling, since Septembre 2022, M. Schreiber, O. Zahm
• PhD in progress: Dominik Huber, “Dynamic Resource Management with MPI Sessions and PMIx” (preliminary title), PhD candidate at the Technical University of Munich (TUM), since 2022, M. Schulz (TUM), M. Schreiber
• PhD in progress: Keerthi Gaddameedi, “Dynamic Resource Management for Parallel-In-Time Simulations” (preliminary title), PhD candidate at the Technical University of Munich (TUM), since 2022, H.-J. Bungartz (TUM), T. Neckel (TUM), M. Schreiber
• PhD in progress: Adama Barry, Plans d’expériences pour la calibration et la validation d’un simulateur numérique, January 2022, F. Bachoc (Institut de Mathématiques de Toulouse), C. Prieur, promoted by M. Munoz Zuniga and S. Bouquet.
• PhD in progress: Ri Wang, Apprentissage statistique pour l’analyse de sensibilité globale avec entrées dépendantes, October 2021, V. Maume-Deschamps (Université Lyon 1), C. Prieur.
• PhD in progress: Romain Verdière, Nonlinear dimension reduction for uncertainty quantification problems, Septembre 2022, O. Zahm
• PhD in progress: Lorenzo Calzolari, Active learning with functional inputs: application to wind turbine reliability design, Novembre 2024, C. Helbert (Ecole Centrale Lyon), C. Prieur, promoted by M. Munoz Zuniga, D. Sinoquet (IFPEN)
• PhD in progress: Katarina Radisic, Prise en compte d'incertitudes externes dans l'estimation de paramètres d'un modèle de transfert d'eau et de pesticides à l'échelle du bassin versant, Université Grenoble-Alpes December 2021, C. Lauvernet (Inrae) and A. Vidard.
• PhD in progress: Hélène Hénon, Assimilation de données variationnelles multi-fidélité pour les prévisions océaniques , Université Grenoble-Alpes Octobre 2023, A. Vidard.
• PhD: Qiao Chen, Low-dimensional structure of ocean data assimilation problems via gradient information, October 2021, defended dec 6th 2024 É. Arnaud and O. Zahm
• PhD: Robin Vaudry, Analyse de Sensibilité, quantification d’incerTitudes et calibRAtion pour des modèles épidémioloGiques structurés, October 2021, defended oct, 24th, 2024, D. Georges (Grenoble INP), C. Prieur 15
• PhD: Clément Duhamel, Inversion robuste d’un code de calcul prenant en entrées des données de nature fonctionnelle. Application à la conception d’éoliennes, October 2020, defended nov, 21st, 2024, C. Helbert (Ecole Centrale Lyon), C. Prieur, promoted by M. Munoz Zuniga, D. Sinoquet (IFPEN) 14
• PostDoc: Alexis Anagnostakis, nov. 2022-nov. 2024, IRGA then Inria funding, Numerical schemes for Sensitivity Analysis of Hypocoercive Systems. C. Prieur.
• Internship (Master 1), Julien Remy “Automatic differentiation with PSyclone”, supervision by M. Schreiber, A. Vidard and M. Brémond
• Internship: Charley Gay, Isaora Bacquet - Conception de supports de médiation scientifique sur l’intelligence artificielle (mythes, fondements et questions éthiques)
• Internship: Maëlys Moro (2024), ENSTA 2nd year internship, PINNs models for optimal control strategies of structured epidemiological models, C. Prieur and D. Georges (GIPSA-Lab)
• Internship: M. Aharmouch (co-encadrement à 50 % avec C. Helbert, Ecole Centrale de Lyon), M2 internship, Active learning for Gaussian processes with functional inputs: application to wind turbine reliability design, C. Helbert, M. Munoz Zuniga, C. Prieur and D. Sinoquet (funded by IFPEN).

10.2.3 Juries

• E. Blayo:
  • June 24, 2024: PhD thesis of Olivier Narinc, Univ. Grenoble Alpes (president)
• Clémentine Prieur:
  • 12 déc. 2024 — PhD thesis of Noé Fellmann, Université Lyon 1 (examinatrice)
  • 12 nov. 2024 — PhD thesis of Jérémy Briant, CERFACS et Université de Toulouse (examinatrice)
  • 21 nov. 2024 — PhD thesis of Clément Duhamel, UGA (directrice de thèse)
  • 24 oct. 2024 — PhD thesis of Robin Vaudry, UGA (directrice de thèse)
  • 3 oct. 2024 — PhD thesis of Paul Lartaud, Institut Polytechnique de Paris (examinatrice)
  • 20 sept. 2024 — PhD thesis of Thi-Nguyen-Khoa Nguyen, ENS-Paris Saclay (examinatrice)
  • 10 juil. 2024 — PhD thesis of Madeleine Kubasch, Institut Polytechnique de Paris (examinatrice)
  • 26 avr. 2024 — PhD thesis of Oumar Balde, Université de Toulouse (rapportrice)
  • 31 jan. 2024 — PhD thesis of Abubakar Haruna, Université Grenoble Alpes (présidente)
  • 12 jan. 2024 — PhD thesis ofd’Eliott Lumet, Université de Toulouse (examinatrice)
• E. Arnaud:
  • member of Inria PhD recruitment committee CORDI-S
  • CSI Jury of Sophie Mauran, PhD in progress at IRIT Toulouse
• A.Vidard:
  • Oct. 4, 2024, PhD thesis of Zoé Lloret, Univ. Paris Saclay, "Un nouveau modèle du transport des gaz à effet de serre dans l’atmosphère mondiale adapté à l’évolution des moyens de calcul à haute performance.", (reviewer).
  • Oct. 8, 2024, PhD thesis of Mathis Peyron, Toulouse INP, "Assimilation de données en espace latent par des techniques de deep learning", (reviewer).
  • Dec. 11, 2024, PhD thesis of Louis Lamérand, Univ. Nice, "Assimilation de données pour la réduction et la calibration de modèles de transport turbulent pour la fusion par confinement magnétique", (reviewer).
• F. Lemarié:
  • Since Nov. 2024: Member of the CE56 scientific evaluation committee of the ANR (French National Research Agency)
  • Dec 10, 2024, PhD thesis of Adrien Garinet, Univ. Toulouse III - Paul Sabatier, Mise en évidence et réduction du mélange numérique dans un modèle numérique incluant la marée interne, un cas d'étude sur l'Asie du Sud-Est
  • PhD thesis of Sofia Flora's, Università degli Studi di Trieste, Superstatistical analysis of HF Radar sea surface currents in the Gulf of Trieste and their idealized deterministic-stochastic modelling (reviewer)
• M.Schreiber:
  • PhD thesis of Fernando Valdés Ravelo, “On explicit exponential integrators in the solution of the elastic equations for the wave propagation”, University of Sao Paulo, 2024
  • PhD thesis of Lucas Meyer, “Online Deep Learning for Numerical Simulations at Scale”, University Grenoble Alpes, 2024
  • PhD thesis of Gaston Irrmann, “Calcul Haute Performance et optimisation de simulations océanographique multi-échelles“, Sorbonne Université, 2024
  • PhD thesis of Pascal Jungblut, “Task Scheduling on FPGA-based Accelerators with Limited Partial Reconfiguration”, Ludwig-Maximilians-Universität München, 2024
  • PhD thesis of Amir Raoofy, “Time Series Mining on High Performance Computing Systems”, Technical University of Munich, 2024

10.3.1 Specific official responsibilities in science outreach structures

• Ch. Kazantsev and E. Blayo are president and vice president respectively of La Grange des Maths

10.3.2 Productions (articles, videos, podcasts, serious games, ...)

• Ch. Kazantsev and E. Blayo are strongly involved in the creation and dissemination of pedagogic suitcases with mathematical activities designed for primary and secondary schools, as well as an escape game. These actions are led in the context of the association La Grange des Maths.
• E. Blayo and A. Vidard have initiated a series of pedagogical videos on numerical ocean modeling, in collaboration with L’Esprit Sorcier TV. The teaser (available here) was launched in October, in the occasion of La Fête de la Science. The five episodes will be published online in the first half of 2025.

10.3.3 Participation in Live events

• E. Blayo gave several outreach talks, in particular for high school students, and for more general audiences.
• Participation to "La fête de la science" E. Arnaud, E. Blayo, H. Brunie, E. Kazantsev, A. Saillet.
• E. Arnaud, Intelligence Artificielle, mythes et réalité - Séminar given at Lycée Villard Bonnot, june 2024
• Clémentine Prieur is regularly taking part to meetings with high school students to promote sciences for young women.

10.3.4 Others science outreach relevant activities

• E. Blayo was the “regional ambassador’’ of the Fête de la Science for the Auvergne-Rhône-Alpes region. In this capacity, he took part in several official events, received media coverage on social networks, and gave interviews for the written press, radio and TV.

International journals

• 1 articleM.Marie Billaud-Friess, A.Arthur Macherey, A.Anthony Nouy, C.Clémentine Prieur and C.Clémentine Prieur. A probabilistic reduced basis method for parameter-dependent problems.Advances in Computational Mathematics502March 2024, 1-22HALDOIback to text
• 2 articleE.Emanuele Borgonovo, E.Elmar Plischke and C.Clémentine Prieur. Total Effects with Constrained Features.Statistics and Computing3487March 2024, 1-29HALDOIback to text
• 3 articleT.Théo Brivoal, G.Guillaume Samson, H.Hervé Giordani, R.Romain Bourdallé-Badie, F.Florian Lemarié and G.Gurvan Madec. Impact of surface current and temperature feedback on kinetic energy over the North-East Atlantic from a coupled ocean / atmospheric boundary layer model.Dynamics of Atmospheres and Oceans107September 2024, 101464HALDOIback to text
• 4 articleP.-A.Pierre-Antoine Dumont, F.Francis Auclair, F.Franck Dumas, Y.Yann Stéphan and L.Laurent Debreu. Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean: Impact of the bottom-boundary condition.Ocean Modelling189June 2024, 102371HALDOI
• 5 articleH. M.Henri Mermoz Kouye, G.Gildas Mazo, C.Clémentine Prieur and E.Elisabeta Vergu. Performing global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology.Computational & Applied Mathematics43409September 2024HALDOIback to text
• 6 articleM. T.Matthew T.C. Li, Y.Youssef Marzouk and O.Olivier Zahm. Principal Feature Detection via $$-Sobolev Inequalities.Bernoulli304November 2024, 2979-3003HALDOIback to text
• 7 articleV.Vera Oerder, F.François Colas, V.Vincent Echevin, S.Sébastien Masson, F.Florian Lemarié and L.Lionel Renault. Impacts of the Mesoscale Ocean‐Atmosphere Coupling on the Peru‐Chile Ocean Dynamics: Impact of the Thermal Feedback.Journal of Geophysical Research. Oceans1296June 2024, e2023JC020351HALDOIback to text
• 8 articleA.Ahmad Tarraf, M.Martin Schreiber, A.Alberto Cascajo, J.-B.Jean-Baptiste Besnard, M.-A.Marc-André Vef, D.Dominik Huber, S.Sonja Happ, A.André Brinkmann, D.David Singh, H.-C.Hans-Christian Hoppe, A.Alberto Miranda, A.Antonio Peña, R.Rui Machado, M.Marta Garcia-Gasulla, M.Martin Schulz, P.Paul Carpenter, S.Simon Pickartz, T.Tiberiu Rotaru, S.Sergio Iserte, V.Victor Lopez, J.Jorge Ejarque, H.Heena Sirwani, J.Jesus Carretero and F.Felix Wolf. Malleability in Modern HPC Systems: Current Experiences, Challenges, and Future Opportunities.IEEE Transactions on Parallel and Distributed Systems359September 2024, 1551-1564HALDOI

Invited conferences

• 9 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Robust calibration of a water and pesticide transfer model at the catchment scale: Consideration of forcing uncertainty on the sensitivity and calibration of a catchment-scale pesticide transfer model.mexico 2024 - Rencontres annuelles du réseau MexicoVilleurbanne, France2024HAL

International peer-reviewed conferences

• 10 inproceedingsV.Valentin Breaz and R.Richard Wilkinson. Randomized Maximum Likelihood via High-Dimensional Bayesian Optimization.2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2024)Seoul, South KoreaIEEEMarch 2024, 5300-5304HALDOI
• 11 inproceedingsS.Simon Clement, F.Florian Lemarié and E.Eric Blayo. Semi-discrete analysis of a simplified air-sea coupling problem with nonlinear coupling conditions.Lecture Notes in Computational Science and EngineeringDD 2022 - 27th International Domain Decomposition Conference149Lecture Notes in Computational Science and EngineeringPrague (CZ), Czech RepublicSpringer Nature Switzerland2024, 141-148HALDOIback to text
• 12 inproceedingsA.-A.Antoine-Alexis Nasser, N. C.Nicolas C. Jourdain, P.Pierre Mathiot and G.Gurvan Madec. Benefits of the Brinkman Volume Penalisation Method for the Ice-Shelf Melt Rates Produced by Z-coordinate Ocean Models.EGU24 - European Geosciences Union General AssemblyVienne, Austria2024HALDOI

Conferences without proceedings

• 13 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Calibration robuste d'un modèle hydrologique de transfert de pesticides par métamodélisation.JMSC 2024 - 5ème édition des Journées de Modélisation des Surfaces ContinentalesStrasbourg, France2024, 1-49HAL

Doctoral dissertations and habilitation theses

• 14 thesisC.Clément Duhamel. Gaussian processes-based excursion set estimation for scalar or vector black box functions. Application to the calibration of a numerical wind turbine simulator..Université Grenoble AlpesNovember 2024HALback to text
• 15 thesisR.Robin Vaudry. Modeling, analysis and simulation of structured complex systems inepidemiology..Université Grenoble - AlpesOctober 2024HALback to text

Reports & preprints

• 16 reportC.Céline Acary-Robert, E.Emmanuel Agullo, L.Ludovic Courtès, M.Marek Felšöci, K.Konrad Hinsen, A.Arun Isaac, O.Ontje Lünsdorf, P.Pjotr Prins, S.Simon Tournier, P.Philippe Virouleau and R.Ricardo Wurmus. Guix-HPC Activity Report 2022–2023.Inria Bordeaux - Sud OuestFebruary 2024, 1-32HAL
• 17 miscA.Alexis Anagnostakis. Pricing and hedging for a sticky diffusion.October 2024HALDOI
• 18 miscV.Vincent Bansaye, P.-Y.Pierre-Yves Boëlle, S.Simon Cauchemez, B.Bernard Cazelles, P.Pascal Crepey, L.Lina Cristancho-Fajardo, J.-S.Jean-Stéphane Dhersin, S.Sorin Dumitrescu, P.Pauline Ezanno, A.Antoine Flahault, J.-L.Jean-Louis Golmard, P.Patrick Hoscheit, H.Henri Mermoz Kouye, M.Madeleine Kubasch, C.Catherine Laredo, A.Alain Mallet, L.Lulla Opatowski, C.Clémentine Prieur and A.Amandine Véber. Hommage à Elisabeta Vergu.2024HAL
• 19 miscA.Adama Barry, F.François Bachoc, S.Sarah Bouquet, M. M.Miguel Munoz Munoz Zuniga and C.Clémentine Prieur. Optimal Design of Physical and Numerical Experiments for Computer Code Calibration.June 2024HALback to text
• 20 miscR.Rishabh Bhatt, L.Laurent Debreu and A.Arthur Vidard. Introducing time parallelisation within data assimilation.January 2025HAL
• 21 reportC.Christophette Blanchet-Scalliet, C.Céline Helbert, D.Delphine Sinoquet, M. M.Miguel Munoz Munoz Zuniga, R.Rodolphe Le Riche, D.Didier Rullière, C.Clémentine Prieur, O.Olivier Zahm, J.Josselin Garnier, D.Dimo Brockhoff, O.Olivier Roustant, F.François Bachoc, L.Luc Pronzato, Y.Yann Richet, J.Jérémy Rohmer, F.Frédéric Huguet, D.David Gaudrie, A.Amandine Marrel, B.Baptiste Kerleguer, T.Thomas Perrillat-Bottonet and C.Cedric Durantin. Activity report ciroquo research & industry consortium.Ecole Centrale de Lyon; Mines Saint-Etienne; Université Toulouse 3 (Paul Sabatier); Stellantis France; BRGM (Bureau de recherches géologiques et minières); CEA; IFP Energies Nouvelles; Institut de Radioprotection et de Sûreté Nucléaire; Storengy; INRIA; CNRS2024, 1-11HAL
• 22 miscV.Valentin Breaz, O.Olivier Zahm and M. M.Miguel Munoz Munoz Zuniga. Literature review on rare event probability estimation in high dimension.April 2024HAL
• 23 miscQ.Qiao Chen, É.Élise Arnaud, R.Ricardo Baptista and O.Olivier Zahm. Coupled input-output dimension reduction: Application to goal-oriented bayesian experimental design and global sensitivity analysis.2024HALback to textback to text
• 24 miscS.Simon Clement, E.Eric Blayo, L.Laurent Debreu, J.-M.Jean-Michel Brankart, P.Pierre Brasseur, L.Long Li and E.Etienne Mémin. Link between stochastic grid perturbation and location uncertainty framework.2024HALback to text
• 25 miscT.Tiangang Cui, X.Xin Tong and O.Olivier Zahm. Optimal Riemannian metric for Poincaré inequalities and how to ideally precondition Langevin dymanics.March 2024HALback to text
• 26 miscS.Sébastien Da Veiga, F.Fabrice Gamboa, A.Agnès Lagnoux, T.Thierry Klein and C.Clémentine Prieur. Efficient estimation of Sobol’ indices of any order from a single input/output sample.2024HALback to text
• 27 miscR.Rafael Flock, Y.Yiqiu Dong, F.Felipe Uribe and O.Olivier Zahm. Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors.August 2024HALback to textback to textback to text
• 28 miscP.Philip Freese, S.Sebastian Götschel, T.Thibaut Lunet, D.Daniel Ruprecht and M.Martin Schreiber. Parallel performance of shared memory parallel spectral deferred corrections.March 2024HAL
• 29 miscD.Dominik Huber, M.Martin Schreiber, M.Martin Schulz, H.Howard Pritchard and D.Daniel Holmes. Design Principles of Dynamic Resource Management for High-Performance Parallel Programming Models.March 2024HALback to text
• 30 miscH. M.Henri Mermoz Kouye, C.Clémentine Prieur and E.Elisabeta Vergu. An extension of Sellke construction and uncertainty quantification for non-Markovian epidemic models.October 2024HALback to text
• 31 miscF.Florian Lemarié. Formulation of a three-dimensional atmospheric boundary layer model for an improved representation of air-sea interactions in eddying oceanic models.March 2024HAL
• 32 miscM. T.Matthew T. C. Li, T.Tiangang Cui, F.Fengyi Li, Y.Youssef Marzouk and O.Olivier Zahm. Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities.2024HAL
• 33 miscS.Sara Mazzonetto and A.Alexis Anagnostakis. On the number of crossings and bouncings of a diffusion at a sticky threshold.October 2024HAL
• 34 miscS.Sara Mazzonetto and A.Alexis Anagnostakis. Sticky-threshold diffusions, local time approximation and parameter estimation.2024HAL
• 35 miscM.Manolis Perrot, F.Florian Lemarié and T.Thomas Dubos. Energetically consistent Eddy-Diffusivity Mass-Flux convective schemes. Part I: Theory and Models..August 2024HALback to text
• 36 miscM.Manolis Perrot and F.Florian Lemarié. Energetically consistent Eddy-Diffusivity Mass-Flux schemes. Part II: implementation and evaluation in an oceanic context..August 2024HALback to textback to text
• 37 miscK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Impact of input forcings variability on the global sensitivity analysis of a hydrological model.December 2024HALback to text
• 38 miscF. V.Fernando V. Ravelo, M.Martin Schreiber and P. S.Pedro S. Peixoto. High-order exponential integration for seismic wave modeling.September 2024HALDOI
• 39 miscJ. G.João Guilherme Caldas Steinstraesser, P. d.Pedro da Silva Peixoto and M.Martin Schreiber. A second-order semi-Lagrangian exponential scheme with application to the shallow-water equations on the rotating sphere.May 2024HAL
• 40 miscM.Manel Tayachi, C.Céline Acary-Robert and E.Eric Blayo. Design and analysis of a Schwarz coupling method for 3D Navier-Stokes equations and 2D Shallow Water equations.2024HAL
• 41 miscV.Victor Trappler and A.Arthur Vidard. State-dependent preconditioning for the inner-loop in Variational Data Assimilation using Machine Learning.2025HALback to text
• 42 miscR.Ri Wang, V.Véronique Maume-Deschamps and C.Clémentine Prieur. Quantile oriented sensitivity analysis with random forest based on pinball loss.June 2024HALback to text
• 43 miscB.Benjamin Zanger, O.Olivier Zahm, T.Tiangang Cui and M.Martin Schreiber. Sequential transport maps using SoS density estimation and $$-divergences.January 2025HALback to textback to textback to text

Other scientific publications

• 44 inproceedingsM.Maurice Brémond, H.Hugo Brunie, L.Laurent Debreu, R. W.Rupert W Ford, F.Florian Lemarié, A.Anna Mittermair, A. R.Andrew R Porter, J.Julien Rémy, P.Philippe Rosales, M.Martin Schreiber, M.Martin Schulz, S.Sergi Siso and A.Arthur Vidard. Poseidon: A Source-to-Source Translator for Holistic HPC Optimizations of Ocean Models on Regular Grids.SC 2024 - International Conference for High Performance Computing, Networking, Storage, and AnalysisAtlanta (Georgia), United States2024, 1-1HALDOI
• 45 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Consideration of uncertain forcings in the global sensitivity analysis and metamodeling of a pesticide transfer model.EGU General Assembly 2024Vienna, Austria, Austria2024, 1-1HALDOI

Software

• 46 softwareS.Simon Clément and L.Long Li. Stochastic Grid Perturbation on Quasi-Geostrophic model.12024 lic: MIT.HALSoftware HeritageVCS