7.1.1 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:
  In 2020, the development of the AGRIF software received the support of 6 months of ATOS-BULL engineer through the European project ESIWACE2. The developments focused on optimizations in the interpolation phases.
• URL:
  https://­gitlab.­inria.­fr/­ldebreu/­agrif
• Publications:
  tel-01546328, hal-00387435
• Contact:
  Laurent Debreu
• Participants:
  Roland Patoum, Laurent Debreu

7.1.2 BALAISE

• Name:
  Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement
• Keywords:
  Multi-scale analysis, Data assimilation, Optimal control
• Functional Description:
  BALAISE (Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement) is a test bed for image data assimilation. It includes a shallow water model, a multi-scale decomposition library and an assimilation suite.
• Contact:
  Patrick Vidard

7.1.3 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

7.1.4 Sensitivity

• Functional Description:
  This package is useful for conducting sensitivity analysis of complex computer codes.
• URL:
  https://­cran.­r-project.­org/­web/­packages/­sensitivity/­index.­html
• Contact:
  Laurent Gilquin

8.1.1 Numerical Schemes for Ocean Modelling

Participants: Eric Blayo, Laurent Debreu, Emilie Duval, Florian Lemarié, Gurvan Madec, Antoine Nasser.

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 favour the use of the non-hydrostatic compressible equations that removes the need for a 3D resolution at the price of reincluding acoustic waves 69.

A comparison between 2D and 3D simulations of non hydrostatic surface waves has been performed in 13.

In addition, Emilie Duval started her PhD in September 2018 on the coupling between the hydrostatic incompressible and non-hydrostatic compressible equations. In 2021, a detailed analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean has been published in Ocean Modelling2.

Accurate and stable implementation of bathymetry boundary conditions in ocean models remains a challenging problem. The dynamics of ocean flow often depend sensitively on satisfying bathymetry boundary conditions and correctly representing their complex geometry. Generalized (e.g. ) terrain-following coordinates are often used in ocean models, but they require smoothing the bathymetry to reduce pressure gradient errors. Geopotential -coordinates are a common alternative that avoid pressure gradient and numerical diapycnal diffusion errors, but they generate spurious flow due to their “staircase” geometry. In 61, we introduce a new Brinkman volume penalization to approximate the no-slip boundary condition and complex geometry of bathymetry in ocean models. This approach corrects the staircase effect of -coordinates, does not introduce any new stability constraints on the geometry of the bathymetry and is easy to implement in an existing ocean model. The porosity parameter allows modelling subgrid scale details of the geometry. We illustrate the penalization and confirm its accuracy by applying it to three standard test flows: upwelling over a sloping bottom, resting state over a seamount and internal tides over highly peaked bathymetry features. New results on realistic applications will be submitted soon. In the context of the Gulf Stream simulation, Figure (1) shows very significant improvements brought by the use of penalization methods. Through the use of penalty methods, the Gulf Stream detachment is correctly represented in a 1/8 degree simulation. This opens the door to a clear improvement of climate models in which a good representation of this mechanism is essential. Following this work, Antoine Nasser started his PhD in October 2019 on penalization methods. One of the objectives is to study the representation of overflows in global ocean model. The NEMO ocean model will be used for the applications.

In the context of the H2020 IMMERSE project, the AIRSEA team is in charge of the development of a new time stepping strategy for the NEMO ocean model. The team also studies the use of exponential time integrators (54 (submitted to Applied Numerical Mathematics) and 4) for ocean models.

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

8.1.2 Coupling Methods for Oceanic and Atmospheric Models and Representation of the Air-Sea Interface

Participants: Eric Blayo, Florian Lemarié, Sophie Thery, Simon Clément.

1. Continuous and discrete analysis of Schwarz algorithms for OA coupling: we 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. In the framework of S. Thery PhD (defended in February 2021) the well-posedness of the non-linear coupling problem including parameterizations has been addressed and a detailed continuous 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 30, 18. In S. Clement PhD, 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 36. Such framework allows to study more complex coupling problems whose formulation is representative of the discretization used in realistic coupled models 60.

   Within the COCOA project, a Schwarz-like iterative method has been applied in a state-of-the-art Earth-System model to evaluate the consequences of inaccuracies in the usual ad-hoc ocean-atmosphere coupling algorithms used in realistic models 14, 43. 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 significant. The objective now is to reduce the computational cost of Schwarz algorithms using deep learning techniques.

2. Representation of the air-sea interface in coupled models: During the PhD-thesis of Charles Pelletier the scope was on including the formulation of physical parameterizations in the theoretical analysis of the coupling, in particular the parameterization schemes to compute air-sea fluxes. Following this work, a novel and rigorous framework for a consistent two-sided modeling of the surface boundary layer has been proposed 15. This framework allows for a more general representation of the vertical physics at the air-sea interface while improving the mathematical regularity of the numerical solutions. Moreover, it is flexible enough to include additional physical parameters for example to account for the effect of surface waves in the turbulent flux computation. This work is the first step toward more adequate discretization methods for the parameterization of surface and planetary boundary layers in coupled models.

   At a more fundamental level, in collaboration with A. Wirth, we have studied turbulent fluctuations in a coupled Ekman layer problem with randomized drag coefficient 20.

3. A simplified atmospheric boundary layer model for oceanic purposes: Part of our activities within the IMMERSE and SHOM 19CP07 projects 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 11. 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 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 5. The next step is to find adequate ways to fill some gaps in the 1D approach either using multiple scales asymptotic techniques or by casting the equations in terms of perturbations around an ambient state given by a large-scale dataset.

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). Our work on ocean-atmosphere coupling has steadily matured over the last few years and has reached a point where it triggers interest from the physicists. Through the funding of the projects ANR COCOA (2017-2021, PI: E. Blayo) and SHOM 19CP07 (2020-2024, PI: F. Lemarié), 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.

8.1.3 Physics-Dynamics coupling: Consistent subgrid-scale modeling

Participants: Florian Lemarié, Manolis Perrot, Simon Clement.

In current models, the scale separation between the resolved part of the flow and the unresolved part is carried out via the Reynolds decomposition which corresponds to a filtering of the Navier-Stokes equations. Such a filtering leads to an evolution equation for the large-scale flow containing unknown terms (often called Reynolds stress terms) which represent the average contribution of the small-scale processes. The system is closed by so-called parameterizations that arbitrarily relate the contribution of small-scale processes to large-scale variables. In this context, the AIRSEA team has started work on two aspects:

1. Energetically consistent discretization of boundary layer parameterizations Part of S. Clement's thesis is about the discretization of boundary layer parameterizations. The problem of interest takes the form of an nonstationary nonlinear parabolic equation. The objective is to derive a discretization for which we could prove nonlinear stability criteria and show robustness to large variations in parabolic Courant number while being consistent with our knowledge of the underlying physical principles (e.g. the Monin-Obukhov theory in the surface layer).
2. 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 approach (a.k.a. Boussinesq Hypothesis). In the framework of the PhD of Manolis Perrot a first step is to study the derivation of mass-flux convection schemes, popular in atmospheric models, to extend them specifically to the oceanic context. This extension to the oceanic context will be carried out under certain "consistency" constraints: energetic considerations, scale-awareness and well-posedness of the resulting model. In a second step, reference LES simulations will be developed to guide the formulation of unknown/uncertain terms in the extended mass-flux scheme.

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, 2020-2024, PI: F. Lemarié) and one on the convection parameterization (Institut des Mathématiques pour la Planètre Terre, 2021-2024, PIs: F. Lemarié and G. Madec).

8.1.4 Nonhydrostatic Modeling

Participant: Eric Blayo, Laurent Debreu, Emilie Duval.

In the context of the French initiative CROCO (Coastal and Regional Ocean COmmunity model, www.croco-ocean.org) for the development of a new oceanic modeling system, Emilie Duval is working on the design of methods to couple local nonhydrostatic models to larger scale hydrostatic ones (PhD started in Oct. 2018). 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). A thorough analysis of the different families of waves that can be present in these equations was performed. Moreover a decomposition of the solutions into vertical modes, which is quite usual in the hydrostatic case, has been generalized in the nonhydrostatic case, which could be an interesting lead for coupling algorithms. A prototype has been implemented, which allows for analytical solutions in simplified configurations and makes it possible to test different numerical approaches.

8.1.5 Machine learning for reconstruction of model parameters.

Participants: Laurent Debreu, Eugene Kazantsev, Arthur Vidard, Olivier Zahm.

Artificial intelligence and machine learning may be considered as a potential way to address unresolved model scales and to approximate poorly known processes such as dissipation that occurs essentially at small scales. In order to understand the possibility to combine numerical model and neural network learned with the aid of external data, we develop a network generation and learning algorithm and use it to approximate nonlinear model operators.

A potential way to reconstruct subgrid scales consists in application the Image Super-Resolution methods that refer to the process of recovering high-resolution images from low-resolution image in computer vision and image processing. Recent years have shown remarkable progress of image super-resolution using machine learning techniques 84. We try to use this methodology in order to identify fine structure of the chaotic turbulent solution of a simple barotropic ocean model. After the learning the flow patterns obtained by the high resolution model, the neuron net can identify fine structure in the low-resolution model solution with better precision than bicubic interpolation.

Different techniques of neuron net construction have been analyzed. Full-connected networks, basic convolutional and encoder-decoder processes 72 as well as mixed architectures were compared with each other and with the classical interpolation of model solution on a low-resolution grid.

8.2.1 Direct assimilation of image sequences

At the present time the observation of Earth from space is done by more than thirty satellites. These platforms provide two kinds of observational information:

• Eulerian information as radiance measurements: the radiative properties of the earth and its fluid envelops. These data can be plugged into numerical models by solving some inverse problems.
• Lagrangian information: the movement of fronts and vortices give information on the dynamics of the fluid. Presently this information is scarcely used in meteorology by following small cumulus clouds and using them as Lagrangian tracers, but the selection of these clouds must be done by hand and the altitude of the selected clouds must be known. This is done by using the temperature of the top of the cloud.

Our current developments are targeted at the use of learning methods methods to describe the evolution of the images. This approach is being applied to the tracking of oceanic oil spills in the framework of a Long Li's Phd in co-supervision with Jianwei Ma. It led to the publication of 12 . In parallel, we investigated the same problem in the framework of pesticide transfer 27

8.2.2 Observation error representation

Accounting for realistic observations errors is a known bottleneck in data assimilation, because dealing with error correlations is complex. Following a previous study on this subject, we propose to use multiscale modelling, more precisely wavelet transform, to address this question. In 59 we investigate the problem further by addressing two issues arising in real-life data assimilation: how to deal with partially missing data (e.g., concealed by an obstacle between the sensor and the observed system); how to solve convergence issues associated to complex observation error covariance matrices? Two adjustments relying on wavelets modelling are proposed to deal with those, and offer significant improvements. The first one consists in adjusting the variance coefficients in the frequency domain to account for masked information. The second one consists in a gradual assimilation of frequencies. Both of these fully rely on the multiscale properties associated with wavelet covariance modelling.

This kind of work was put to application in a collaboration with colleagues of LGGE and led to the publication of 10

In the meantime, STORM, a new collaborative project with Université de La Réunion started this year 53. Our role is to prepare for the assimilation of data collected by sea turtles., and in particular work on the description of observation error statistics.

8.3.1 Parameter space dimension reduction and Model order reduction

Participants: Arthur Macherey, Youssef Marzouk, Clémentine Prieur, Alessio Spantini, Ricardo Baptista, Daniele Bigoni, Olivier Zahm.

Numerical models describing the evolution of the system (ocean + atmosphere) or any numerical models describing the evolution of a complex dynamical system (e.g., the evolution of a pandemic) contain a large number of parameters which are generally poorly known. The reliability of the numerical simulations strongly depends on the identification and calibration of these parameters from observed data. In this context, it seems important to understand the kinds of low-dimensional structure that may be present in geophysical models and to exploit this low-dimensional structure with appropriate algorithms. We focus in the team, on parameter space dimension reduction techniques, reduced bases, low-rank structures and transport maps techniques for probability measure approximation.

In 34 we introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{ℝ}^d\to ℝ$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{ℝ}^d\to {ℝ}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{ℝ}^m\to ℝ$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm makes use of a sample ${\{x^{\left(i\right)},u\left(x^{\left(i\right)}\right),\nabla u\left(x^{\left(i\right)}\right)\}}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set. This work was conducted in the framework of the Inria associate team UNQUESTIONABLE, in collaboration with Youssef Marzouk (MIT, US).

In 37 we present a novel offline-online method to mitigate the computational burden of the characterization of conditional beliefs in statistical learning. In the offline phase, the proposed method learns the joint law of the belief random variables and the observational random variables in the tensor-train (TT) format. In the online phase, it utilizes the resulting order-preserving conditional transport map to issue real-time characterization of the conditional beliefs given new observed information. Compared with the state-of-the-art normalizing flows techniques from machine learning, the proposed method relies on function approximation and is equipped with thorough performance analysis. This also allows us to further extend the capability of transport maps in challenging problems with high-dimensional observations and high-dimensional belief variables. On the one hand, we present novel heuristics to reorder and/or reparametrize the variables to enhance the approximation power of TT. On the other, we integrate the TT-based transport maps and the parameter reordering/reparametrization into layered compositions to further improve the performance of the resulting transport maps. We demonstrate the efficiency of the proposed method on various statistical learning tasks in ordinary differential equations (ODEs) and partial differential equations (PDEs).

Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions and for efficiently performing inference. While the problem of learning graph structure from data has been studied extensively for certain parametric families of distributions, most existing methods fail to consistently recover the graph structure for non-Gaussian data. In 32, we propose an algorithm for learning the Markov structure of continuous and non-Gaussian distributions. To characterize conditional independence, we introduce a score based on integrated Hessian information from the joint log-density, and we prove that this score upper bounds the conditional mutual information for a general class of distributions. To compute the score, our algorithm SING estimates the density using a deterministic coupling, induced by a triangular transport map, and iteratively exploits sparse structure in the map to reveal sparsity in the graph. For certain non-Gaussian datasets, we show that our algorithm recovers the graph structure even with a biased approximation to the density. Among other examples, we apply sing to learn the dependencies between the states of a chaotic dynamical system with local interactions.

In a joint work 44 with Didier Georges (GIPSA Lab, Grenoble) and Mathieu Oliver (internship student), we proposed a spatialized extension of a SIR model that accounts for undetected infections and recoveries as well as the load on hospital services. The spatialized compartmental model we introduced is governed by a set of partial differential equations (PDEs) defined on a spatial domain with complex boundary. We proposed to solve the set of PDEs defining our model by using a meshless numerical method based on a finite difference scheme in which the spatial operators were approximated by using radial basis functions. Then we calibrated our model on the French department of Isère during the first period of lockdown, using daily reports of hospital occupancy in France. Our methodology allowed to simulate the spread of Covid-19 pandemic at a departmental level, and for each compartment. However, the simulation cost prevented from online short-term forecast. Therefore, we proposed to rely on reduced order modeling tools to compute short-term forecasts of infection number. The strategy consisted in learning a time-dependent reduced order model with few compartments from a collection of evaluations of our spatialized detailed model, varying initial conditions and parameter values. A set of reduced bases was learnt in an offline phase while the projection on each reduced basis and the selection of the best projection was performed online, allowing short-term forecast of the global number of infected individuals in the department.

In the framework of Arthur Macherey’s PhD (defended in June 2021), in collaboration with Anthony Nouy and Marie Billaud-Friess (Ecole Centrale Nantes), we have proposed algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation 52. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. We are now interested in solving parametrized PDE with stochastic algorithms in the framework of potentially high dimensional parameter space. A preliminary step was the development of a PAC algorithm in relative precision for bandit problem with costly sampling 35.

Reduced models are also developed In the framework of robust inversion. In 62, we have combined a new greedy algorithm for functional quantization with a Stepwise Uncertainty Reduction strategy to solve a robust inversion problem under functional uncertainties. In a more recent work, we further reduced the number of simulations required to solve the same robust inversion problem, based on Gaussian process meta-modeling on the joint input space of deterministic control parameters and functional uncertain variable 39. These results are applied to automotive depollution. This research axis was conducted in the framework of the Chair OQUAIDO. This research axis is till active in the team through Clément Duhamel’s PhD, in collaboration with Céline Helbert (Ecole Centrale Lyon) and Miguel Munoz Zuniga, Delphine Sinoquet (IFPEN, Rueil Malmaison).

8.4.1 Variational data assimilation and parallel in time methods

Participants: Rishabh Bhatt, Laurent Debreu, Arthur Vidard.

Rishabh Bhatt started his PhD in December 2019. Under the supervision of Laurent Debreu and Arthur Vidard, he studies the application of time parallelization algorithms to variational data assimilation methods. Thus, at each step of the optimization algorithm, the direct model is integrated by a time-parallel method (here the Parareal algorithm 76). One of the main difficulties lies in the choice of the stopping criterion of the Parareal algorithm. To do so, we rely on theoretical results on the convergence of conjugate gradient methods in the presence of approximate gradient calculations 65. The first results are encouraging and show the possibility to optimally tune the stopping criterion of the Parareal algorithm (and thus the number of iterations) without affecting the convergence of the conjugate gradient. These results are reported in (33). We are now working on taking better advantage of the coupling of these two iterative methods (conjugate gradient and Parareal), in particular by optimally reusing the Krylov bases of the Krylov Enhanced version of the Parareal algorithm.

Scientific context

Forecasting geophysical  systems require complex models, which sometimes need to be coupled, and which make use of data assimilation. The objective of this project is, for a given output of such a system, to identify the most influential parameters, and to evaluate the effect of uncertainty in input parameters on model output. Existing stochastic tools are not well suited for high dimension problems (in particular time-dependent problems), while deterministic tools are fully applicable but only provide limited information. So the challenge is to gather expertise on one hand on numerical approximation and control of Partial Differential Equations, and on the other hand on stochastic methods for sensitivity analysis, in order to develop and design innovative stochastic solutions to study high dimension models and to propose new hybrid approaches combining the stochastic and deterministic methods. We took part to the writing of a position paper on the futur of sensitivity analysis 17.

8.5.1 Global sensitivity analysis

Participants: Elise Arnaud, Eric Blayo, Laurent Gilquin, Maria Belén Heredia, Adrien Hirvoas, Alexandre Janon, Henri Mermoz Kouye, Clémentine Prieur, Laurence Viry, Arthur Vidard, Emilie Rouzies.

8.5.2 Global sensitivity analysis with dependent inputs

An important challenge for stochastic sensitivity analysis is to develop methodologies which work for dependent inputs. Recently, the Shapley value, from econometrics, was proposed as an alternative to quantify the importance of random input variables to a function. Owen 79 derived Shapley value importance for independent inputs and showed that it is bracketed between two different Sobol' indices. Song et al. 82 recently advocated the use of Shapley value for the case of dependent inputs. In a recent work 78, in collaboration with Art Owen (Standford's University), we showed that Shapley value removes the conceptual problems of functional ANOVA for dependent inputs. We also investigated further the properties of Shapley effects in 71. By the end of 2021, Clémentine Prieur started a collaboration with Elmar Plischke (TU Clausthal, Germany) and Emanuele Borgonovo (Bocconi University, Milan, Italy) to estimate total Sobol’ indices as a measure for variable selection even in the framework of dependent inputs. In particular, it allows to estimate total Sobol’ indices for inputs defined on a non rectangular domain. This setting is of particular interest for applications where the input space is reduced due to physical constraints on the quantity of interest. This last setting was encountered, e.g., in Maria Belén Heredia’s PhD thesis (defended in december, 2020), and analyzed by estimating Shapley effects with a nonparametric procedure based on nearest neighbors 50 (see Section 8.5.4 for more details). In October 2021, Ri Wang has started a PhD, cosupervised by Clémentine Prieur and Véronique Maume-Deschamps (ICJ, Lyon 1) on the estimation of quantile oriented sensitivity indices in the framework of dependent inputs, by means of random forests or other machine learning tools. Ri Wang has received a funding from the Chinese Scientific Council.

8.5.3 Iterative estimation of Sobol’ indices

Participants: Elise Arnaud, Laurent Gilquin, Clémentine Prieur.

In the field of sensitivity analysis, Sobol’ indices are widely used to assess the importance of the inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol’ estimates. We proposed to tackle this issue by rendering the replication procedure iterative 7. The idea is to enable the addition of new model evaluations to progressively increase the accuracy of the estimates. These evaluations are done at points located in under-explored regions of the experimental designs, but preserving their characteristics. The key feature of this approach is the construction of nested space-filling designs. For the estimation of first-order indices, a nested Latin hypercube design is used. For the estimation of closed second-order indices, two constructions of a nested orthogonal array design are proposed. Regularity and uniformity properties of the nested designs are studied.

8.5.4 Green sensitivity for multivariate and functional outputs

Participants: María Belén Heredia, Clémentine Prieur.

Another research direction for global SA algorithm starts with the report that most of the algorithms to compute sensitivity measures require special sampling schemes or additional model evaluations so that available data from previous model runs (e.g., from an uncertainty analysis based on Latin Hypercube Sampling) cannot be reused. One challenging task for estimating global sensitivity measures consists in recycling an available finite set of input/output data. Green sensitivity, by recycling, avoids wasting. These given data have been discussed, e.g., in 80, 81. Most of the given data procedures depend on parameters (number of bins, truncation argument…) not easy to calibrate with a bias-variance compromise perspective. Adaptive selection of these parameters remains a challenging issue for most of these given-data algorithms. In the context of María Belén Heredia’s PhD thesis, we have proposed 3 a non-parametric given data estimator for aggregated Sobol’ indices, introduced in 73 and further developed in 64 for multivariate or functional outputs. We also introduced aggregated Shapley effects and we have extended a nearest neighbor estimation procedure to estimate these indices 50. We also started a collaboration with Sébastien Da Veiga (Safran Tech), Agnès Lagnoux, Thierry Klein and Fabrice Gamboa (Institut de Mathématiques de Toulouse) on a new nonparametric estimation procedure for closed Sobol’ indices of any order based on degenerate U-statistics.

8.5.5 Global sensitivity analysis for parametrized stochastic differential equations

Participants: Henri Mermoz Kouye, Clémentine Prieur.

Many models are stochastic in nature, and some of them may be driven by parametrized stochastic differential equations (SDE). It is important for applications to propose a strategy to perform global sensitivity analysis (GSA) for such models, in presence of uncertainties on the parameters. In collaboration with Pierre Etoré (DATA department in Grenoble), Clémentine Prieur proposed an approach based on Feynman-Kac formulas 63. The research on GSA for stochastic simulators is still ongoing, first in the context of the MATH-AmSud project FANTASTIC (Statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations) with Chile and Uruguay, secondly through the PhD thesis of Henri Mermoz Kouye, co-supervised by Clémentine Prieur, in collaboration with Gildas Mazo and Eliza Vergu (INRAE, département MIA, Jouy). Note that our recent developments with P. Etoré on GSA for parametrized SDEs and are strongly related to reduced order modeling (see Section 8.3), as GSA requires jose leon intensive computations of the quantity of interest. In collaboration with Pierre Etoré and Joël Andrepont (master internship started in spring 2021), Clémentine Prieur is working on GSA for parametrized SDEs based on Fokker-Planck equation and kernel based sensitivity indices. Note that a joint work between Pierre Etoré, Clémentine Prieur and Jose R. Leon has been submitted, related to exact or approximated computation of Kolmogorov hypoelliptic equations (KHE). Even if not dealing with GSA, it could be a starting point for analyzing sensitivity for models described by a parametrized version of KHE. Concerning Henri Mermoz Kouye’s PhD thesis, the approach is different. We are interested in GSA for compartmental stochastic models. Our methodology relies on a deterministic representation of continuous time Markov chains stochastic compartmental models.

8.5.6 Sensitivity analysis in pesticide transfer models

Participants: Arthur Vidard, Emilie Rouzies, Katarina Radisic.

Pesticide transfer models are valuable tools to predict and prevent pollution of water bodies. However, using such models in operational contexts requires a strong knowledge of their structure including influential parameters. This project aims at performing global sensitivity analysis (GSA) of the PESHMELBA model (pesticide and hydrology: modelling at the catchment scale). This work is made hard due to the modular, complex structure of the model that couples different physical processes. It results in a large input space dimension and a high computational cost that limits the number of available runs. Using classical GSA tools such as Sobol' indices is thus not feasible. In order to circumvent those limitations, we also explored alternative techniques such as HSIC dependence measure or Random Forest metamodel. The use of such methods in the specific context of spatially distributed output was presented in 28 and submitted in a journal paper 46. We extended this work to spatiotemporal output, as presented in 25.

To conclude Section 8.5, let us mention that Clémentine Prieur took part to the writing on a monography on recent trends in sensitivity analysis, which appeared by the end of 2021 29.

8.6.1 Bayesian calibration

Physically-based avalanche propagation models must still be locally calibrated to provide robust predictions, e.g. in long-term forecasting and subsequent risk assessment. Friction parameters cannot be measured directly and need to be estimated from observations. Rich and diverse data is now increasingly available from test-sites, but for measurements made along ow propagation, potential autocorrelation should be explicitly accounted for. In the context of María Belén Heredia’s PhD, in collaboration with IRSTEA Grenoble, we have proposed in 68 a comprehensive Bayesian calibration and statistical model selection framework with application to an avalanche sliding block model with the standard Voellmy friction law and high rate photogrammetric images. An avalanche released at the Lautaret test-site and a synthetic data set based on the avalanche were used to test the approach. Results have demonstrated i) the efficiency of the proposed calibration scheme, and ii) that including autocorrelation in the statistical modelling definitely improves the accuracy of both parameter estimation and velocity predictions. In the context of the energy transition, wind power generation is developing rapidly in France and worldwide. Research and innovation on wind resource characterisation, turbin control, coupled mechanical modelling of wind systems or technological development of offshore wind turbines floaters are current research topics. In particular, the monitoring and the maintenance of wind turbine is becoming a major issue. Current solutions do not take full advantage of the large amount of data provided by sensors placed on modern wind turbines in production. These data could be advantageously used in order to refine the predictions of production, the life of the structure, the control strategies and the planning of maintenance. In this context, it is interesting to optimally combine production data and numerical models  in order to obtain highly reliable models of wind turbines. This process is of interest to many industrial and academic groups and is known in many fields of the industry, including the wind industry, as "digital twin”. The objective of Adrien Hirvoas's PhD work is to develop of data assimilation methodology to build the "digital twin" of an onshore wind turbine. Based on measurements, the data assimilation should allow to reduce the uncertainties of the physical parameters of the numerical model developed during the design phase to obtain a highly reliable model. Various ensemble data assimilation approches are currently under consideration to address the problem.  In the context of this work, it is necessary to develop algorithms of identification quantifying and ranking all the uncertainty sources. This work in done in collaboration with IFPEN. A first paper has been accepted for publication 8.

8.6.2 Simulation & Estimation of EPIdemics with Algorithms

Participants: Clémentine Prieur.

Due to the sanitary context, Clémentine Prieur decided to join a working group, SEEPIA Simulation & Estimation of EPIdemics with Algorithms, animated by Didier Georges (Gipsa-lab). A first work has been published 67. An extension of the classical pandemic SIRD model was considered for the regional spread of COVID-19 in France under lockdown strategies. This compartment model divides the infected and the recovered individuals into undetected and detected compartments respectively. By fitting the extended model to the real detected data during the lockdown, an optimization algorithm was used to derive the optimal parameters, the initial condition and the epidemics start date of regions in France. Considering all the age classes together, a network model of the pandemic transport between regions in France was presented on the basis of the regional extended model and was simulated to reveal the transport effect of COVID-19 pandemic after lockdown. Using the the measured values of displacement of people mobilizing between each city, the pandemic network of all cities in France was simulated by using the same model and method as the pandemic network of regions. Finally, a discussion on an integro-differential equation was given and a new model for the network pandemic model of each age was provided. As already mentioned in Section 8.3, Clémentine Prieur went on working on the pandemic, in collaboration with Didier Georges (GIPSA Lab, Grenoble). Both of them supervised the internship of Matthieu Oliver, submitting a work proposing time-dependent reduced order modeling for short-term forecast from a spatialized SIR model 44. Robin Vaudry started in October 2021 a PhD, funded by the CNR research platform MODCOV19, and cosupervised by Clémentine Prieur and Didier Georges. The objective of this PhD is to solve inverse problems related to spatialized and ages structured commpartmental models of COVID19 pandemic.

8.6.3 Non-Parametric statistical inference for Kinetic Diffusions

Participants: Clémentine Prieur, Jose Raphael Leon Ramos.

This research is the subject of a collaboration with Chile and Uruguay. More precisely, we started working with Venezuela. Due to the crisis in Venezuela, our main collaborator on that topic moved to Uruguay.

We are focusing our attention on models derived from the linear Fokker-Planck equation. From a probabilistic viewpoint, these models have received particular attention in recent years, since they are a basic example for hypercoercivity. In fact, even though completely degenerated, these models are hypoelliptic and still verify some properties  of coercivity, in a broad sense of the word. Such models often appear in the fields of mechanics, finance and even biology. For such models we believe it appropriate  to build statistical non-parametric estimation tools. Initial results have been obtained for the estimation of invariant density, in conditions guaranteeing its existence and unicity 56 and when only partial observational data are available. A paper on the non parametric estimation of the drift has been accepted recently 57 (see Samson et al., 2012, for results for parametric models). As far as the estimation of the diffusion term is concerned, a paper has been accepted 57, in collaboration with J.R. Leon (Montevideo, Uruguay) and P. Cattiaux (Toulouse). Recursive estimators have been also proposed by the same authors in 58, also recently accepted. In a recent collaboration with Adeline Samson from the statistics department in the Lab, we considered adaptive estimation, that is we proposed a data-driven procedure for the choice of the bandwidth parameters.

In 55, we focused on damping Hamiltonian systems under the so-called fluctuation-dissipation condition. Idea in that paper were re-used with applications to neuroscience in 75.

Note that Professor Jose R. Leon (Caracas, Venezuela, Montevideo, Uruguay) was funded by an international Inria Chair, allowing to collaborate further on parameter estimation.

We recently proposed a paper on the use of the Euler scheme for inference purposes, considering reflected diffusions. This paper could be extended to the hypoelliptic framework.

We also have a collaboration with Karine Bertin (Valparaiso, Chile), Nicolas Klutchnikoff (Université Rennes) and Jose R. León (Montevideo, Uruguay) funded by a MATHAMSUD project (2016-2017) and by the LIA/CNRS (2018). We are interested in new adaptive estimators for invariant densities on bounded domains 51, and would like to extend that results to hypo-elliptic diffusions. More recently, in relation with her work on GSA for parametrized SDEs (see Section 8.5.5), Clémentine Prieur is interested in proposing and analyzing theoretical properties of reduced order modeling (see Section 8.3) based on weak formulations of stationary Fokker Planck equations related to hypoelliptic SDEs. This is a collaboration with Pierre Etoré (LJK, département DATA).

8.6.4 Parameter control in presence of uncertainties: robust estimation of bottom friction

Participants: Victor Trappler, Arthur Vidard, Elise Arnaud, Laurent Debreu.

Many physical phenomena are modelled numerically in order to better understand and/or to predict their behaviour. However, some complex and small scale phenomena can not be fully represented in the models. The introduction of ad-hoc correcting terms, can represent these unresolved processes, but they need to be properly estimated.

A good example of this type of problem is the estimation of bottom friction parameters of the ocean floor. This is important because it affects the general circulation. This is particularly the case in coastal areas, especially for its influence on wave breaking. Because of its strong spatial disparity, it is impossible to estimate the bottom friction by direct observation, so it requires to do so indirectly by observing its effects on surface movement. This task is further complicated by the presence of uncertainty in certain other characteristics linking the bottom and the surface (eg boundary conditions). The techniques currently used to adjust these settings are very basic and do not take into account these uncertainties, thereby increasing the error in this estimate.

Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of uncertainties, the minimisation is not straightforward, as the output of the model depends on those uncontrolled inputs and on the control parameter as well. That is why we will aim at minimising the objective function, to get an estimation of the control parameter that is robust to the uncertainties.

The definition of robustness differs depending of the context in which it is used. In this work, two different notions of robustness are considered: robustness by minimising the mean and variance, and robustness based on the distribution of the minimisers of the function. This information on the location of the minimisers is not a novel idea, as it had been applied as a criterion in sequential Bayesian optimisation. However, the constraint of optimality is here relaxed to define a new estimate. To evaluate this estimation, a toy model of a coastal area has been implemented. The control parameter is the bottom friction, upon which classical methods of estimation are applied in a simulation-estimation experiment. The model is then modified to include uncertainties on the boundary conditions in order to apply robust control methods. This was the topic of Victor Trappler's PhD 31.

This work will be continued in two different actions : On the application side, in the framework of an Inrae/Inria collaboration for dealing with pesticide transfer parameterisation, and on the methodological side, in the framework of the joint-lab with ATOS, in order to explore the use of Machine Learning techniques for such problem.

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

10.1.2 Informal International Partners

Clémentine Prieur is PI of MATH-AmSud project 2020-2021 FANTASTIC (Statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations). This project involves Chile (local head Karine Bertin, Universidad de Valparaíso) and Uruguay (local head Jose R. Leon, Universdad de la república de Uruguay, Montevideo).

10.2.1 FP7 & H2020 projects

10.2.2 Other european programs/initiatives

• Program: C3S
• Project acronym: ERGO
• Project title: Enabling an Ensemble of Data Assimilation for the Ocean
• Duration: Février 2019 - juillet 2021
• Coordinator: Arthur Vidard
• Other partners: Cerfacs (France), Met Office (U.K.), CMRE (int, Italie)
• 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.

10.4.1 ANR

• A 4.5-year contract: ANR COCOA (COmprehensive Coupling approach for the Ocean and the Atmosphere). PI: E. Blayo. (Jan. 2017 - Sep. 2021). Other partners: Laboratoire des Sciences du Climat et de l'Environnement (UMR8212, Gif-sur-Yvette), Laboratoire de Météorologie Dynamique (UMR8539, Paris), Laboratoire d'Océanographie Physique et Spatiale (UMR6523, Brest), Centre National de Recherche Météorologique (UMR3589, Toulouse), Cerfacs (Toulouse). This project aims at revisiting the overall representation of air-sea interactions in coupled ocean-atmosphere models, and particularly in climate models, by coherently considering physical, mathematical, numerical and algorithmic aspects.
• A 4-year contract: ANR ADOM (Asynchronous Domain decomposition methods) anr.fr/Projet-ANR-18-CE46-0008
• A 5-year contract: ANR MELODY (Bridging geophysics and MachinE Learning for the modeling, simulation and reconstruction of Ocean DYnamic) anr.fr/Projet-ANR-19-CE46-0011

• A 4-year contract: ANR MODENA, "Model and data reduction for efficient assimilation", PI: Olivier ZAHM The reliability of numerical predictions strongly rely on our ability to calibrate the unknown model parameters using observable data. Data assimilation is a particularly challenging task in ocean modelling because of the complexity of the computational models and because of the high-dimension of both the parameters and the data. The objective of this project is to explore novel methodologies to improve the probabilistic description of the Bayesian solution to inverse problem while, at the same time, taking into consideration the computational limitations imposed by large scale applications. This project relies on three building blocks and on their interplay:

  1. transport maps as a novel approximation tool of complex probability densities,
  2. reduced order models to alleviate the computational burden of expensive models and
  3. dimension reduction to concentrate the computational efforts onto the most relevant directions.

  In addition, the proposed methodology addresses key challenges present in many real-world applications and therefore we expect that they can find applications in other domains.

• A 5-year contract with the French Navy (SHOM) on the improvment of the CROCO ocean model www.croco-ocean.org.
• C. Prieur and E. Arnaud are involved as experts in project High-Tune www.agence-nationale-recherche.fr/Projet-ANR-16-CE01-0010 funded by ANR.

10.4.2 Inria Challenge

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

10.4.3 Other Initiatives

• C. Prieur is co-advising the PhD thesis of Henri Mermoz Kouye, in the framework of the Inria-INRA partnership.
• C. Prieur chaired GdR MASCOT NUM 2010-2017, in which are also involved M. Nodet, E. Blayo, C. Helbert, E. Arnaud, L. Viry, S. Nanty, L. Gilquin. She is still strong involved in the group (co-chair). In particular, she will co-chair next GdR annual meeting in Aussois (May 2020, reported to April 2021). www.gdr-mascotnum.fr/doku.php.
• 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).

11.1.1 Scientific events: selection

11.1.2 Journal

11.1.3 Invited talks

• Clémentine Prieur was invited as plenary speaker of NASPDE 2020, Numerical Analysis of Stochastic PDEs, CIRM, Luminy (France), November, 5-6, 2020 (reported to November, 4-5, 2021).
• Clémentine Prieur was invited as plenary speaker of the 3th International Workshop on Rare-Event Simulation, Paris (France), May, 26-29, 2020 (reported to May, 18-21, 2021)
• Clémentine Prieur was invited as plenary speaker of the 18th International Workshop on Quality Improvements Methods, Dortmund (Germany), June 26-27, 2020 (cancelled).
• Clémentine Prieur was invited as plenary speaker of the SWGEN 2020 Conference on Stochastic Weather Generators, Lyon (France), June 17-19, 2020 (cancelled).
• F. Lemarié: école IMPT impacts morphologiques du changement climatique, Lyon, Nov. 2021 24
• F. Lemarié: 16th U.S. National Congress on Computational Mechanics, Chicago, Jul. 2021 23

11.1.4 Leadership within the scientific community

• L. Debreu is the chair of the CNRS-INSU research program LEFE-MANU on mathematical and numerical methods for ocean and atmosphere insu.cnrs.fr/fr/methodes-mathematiques-et-numeriques-manu since April 2018.
• F. Lemarié is the co-leader with Mike Bell (UK Met Office) of the NEMO (www.nemo-ocean.eu) Working Group on numerical kernel development.

11.1.5 Scientific expertise

• L. Debreu is a member of the steering committee of the CROCO ocean model www.croco-ocean.org
• F. Lemarié is a member of the CROCO (www.croco-ocean.org) scientific committee in charge of the « numerical methods » topic.

11.1.6 Research administration

• E. Blayo is a deputy director of the Jean Kuntzmann Lab.
• C. Prieur is local correspondant in Grenoble for the Mathematical Society of France (SMF).  
• C. Prieur is a member of the MSTIC pole council of UGA.
• C. Prieur is responsible for the applied math speciality for doctoral school MSTII edmstii.univ-grenoble-alpes.fr/
• E. Arnaud is in charge of the AMAC (Algorithmes, Modeles, Analyses, Calcul) department of the Jean Kuntzmann Lab.

11.2.1 Teaching

• Licence (ou équivalent) : E. Arnaud, Mathematics for engineers, 20h, L2, UGA, France
• Licence (ou équivalent) : E. Blayo, Mathematical analysis, 105h, L1, University Grenoble Alpes, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques approfondies pour l'ingénieur, 72h, L2, UGA, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques pour les sciences de l'ingénieur, 81h, L2, UGA, France
• Master (ou équivalent) : E. Arnaud, Statistics, 30h, M1, UGA, France
• Master (ou équivalent) : E. Arnaud, Supervision of student in apprenticeship, 30h, M2, UGA, France
• Master (ou équivalent) : E. Blayo, Partial Differential Equations, 45h, M1, University Grenoble Alpes, France
• E-learning : Mooc Inria Impacts environnementaux du numérique : E. Blayo, "La modélisation numérique, un outil devenu central pour l'environnement"
• E-learning : E. Arnaud is in charge of the pedagogic platform math@uga : implementation of a collaborative moodle platform math.u-ga.fr to share pedagogical resources within teachers and towards students.

11.2.2 Supervision

• PhD: Victor Trappler, Parameter control in presence of uncertainties, Université Grenoble-Alpes, defended June 11th 2021, E. Arnaud, L. Debreu and A. Vidard. 31
• PhD: Sophie Théry, Numerical study of ocean-atmosphere coupling algorithms with boundary layer parameterizations, Université Grenoble Alpes, 10 February 2021, E. Blayo and F. Lemarié.30
• PhD: Arthur Macherey, Uncertainty quantification methods for models described by stochastic differential equations or partial differential equations with a probabilistic interpretation, June, 2021, M. Billaud-Friess, A. Nouy (Ecole Centrale Nantes), C. Prieur 77  
• PhD: Adrien Hirvoas, Development of a data assimilation method for the calibration and continuous update of wind turbines digital twins, March, 2021, E. Arnaud, C. Prieur, promoted by F. Caleyron (IFPEN) 70
• PhD in progress : Emilie Duval, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2018, L. Debreu and E. Blayo.
• PhD in progress : Antoine Nasser, Volume penalization methods for the representation of flows along topography in 3D ocean models, October 2019, L. Debreu and G. Madec.
• PhD in progress : Rishabh Bhatt, Asynchronousparallel in time schemes for data assimilation, December 2019, L. Debreu and A. Vidard.
• PhD in progress: Emilie Rouziès, Assimilation of multi-source data in a pesticide transfer model in a small agricultural watershed, Université Grenoble-Alpes, December 2019, C. Lauvernet (Inrae) and A. Vidard.
• 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: Simon Clément, Numerical analysis for reconciling in space and time the air-sea exchanges and their parameterization. October 2019, E. Blayo and F. Lemarié.
• PhD in progress: Manolis Perrot, Consistent subgrid scale modeling for oceanic climate models. October 2021, E. Blayo and F. Lemarié.    
• 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 : Robin Vaudry, Analyse de Sensibilité, quantification d'incerTitudes et calibRAtion pour des modèles épidémioloGiques structurés, October 2021, D. Georges (Grenoble INP), C. Prieur.    
• PhD in progress : 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, C. Helbert (Ecole Centrale Lyon), C. Prieur, promoted by M. Munoz Zuniga, D. Sinoquet (IFPEN)     
• PhD in progress : Henri Mermoz Kouye, Analyse de sensibilité basée sur les indices de Sobol' pour modèles à sorties stochastiques et fonctionnelles, Octobre 2019, G. Mazo, E. Vergu (INRAE, MIA, Jouy), C. Prieur    
• PhD in progress : Qiao CHEN, Low-dimensional structure of ocean data assimilation problems via gradient information, Octobre 2020 (encadrement : Olivier ZAHM et Élise Arnaud)    
• PhD in progress : Rafael Floch, Dimension reduction of large-scale linear Bayesian inverse problems, Octobre 2020 (encadrement : Olivier ZAHM et Yiqiu DONG)
• Post Doc : Anass El Aouni, Multi-resolution techniques for ocean data assimilation, October 2019, October 2021, A. Vidard

11.2.3 Juries

• E. Blayo:
  • Jan. 12, 2021: PhD thesis of Dimitri Mottet, Institut National Polytechnique de Toulouse (reporter)
  • Mar. 30, 2021: PhD thesis of Adrien Hirvoas, University Grenoble Alpes (president)
  • May 4, 2021: HDR thesis of Julien Le Sommer, University Grenoble Alpes (examiner)
  • Jun. 22, 2021: PhD thesis of Cyril Bozonnet, University Grenoble Alpes (president)
  • Dec. 7, 2021: PhD thesis of Meryl Wimmer, Université Toulouse III Paul Sabatier (reporter)
  • Dec. 13, 2021: PhD thesis of Camille Besombes, Institut National Polytechnique de Toulouse (reporter)
• C. Prieur is the president of the jury of Prix de thèse AMIES (2020-…).
• E. Arnaud : participation to the PhD committee of Emilie Rouziès, UGA INRAE.

11.3.1 Internal or external Inria responsibilities

• F. Lemarié is a member of the local "comité des emplois scientifiques" (CES) (since Sept 2019)
• F. Lemarié is the local scientific correspondent for national calls for projects (since July 2020)
• E. Arnaud : member of Inria PhD recruitment committee CORDI-S
• E. Arnaud : in charge of ATER recruitment committee in computer science of UFR IM2AG, UGA
• E. Arnaud : in charge of the parity commission at Jean Kuntzmann Lab
• E.Kazantsev is a member of the Local Commission for Permanent Formation of Inria Grenoble - Rhône-Alpes.
• F. Lemarié gave a talk at the "Parlons Europe s01e07" internal meeting.

11.3.2 Articles and contents

• Clémentine Prieur took part to a webcast on The Future of Sensitivity Analysis for Systems Modelling and Policy Support www.youtube.com
• Clémentine Prieur gave interviews as a CNRS expert (Figaro, Hoffpost, RCF) on the evolution of COVID19 pandemic.
• C. Prieur was placed on a list of experts who could answer questions on various aspects of the news related to the ongoing Covid-19 epidemic by the CNRS press office. This list is made available to journalists in order to direct them to the appropriate interlocutors according to the angle of their questions.

11.3.3 Education

• C. Kazantsev and E. Blayo are strongly involved in the creation and dissemination of pedagogic suitcases with mathematical activities designed for primary and secondary schools used by about 4,000 pupils in 2020-2021, despite the sanatory crisis. This is done in collaboration with the Rectorat de Grenoble.
• C. Kazantsev is a member of an IREM group for creation of scientific activities for professional development of secondary schools teachers.
• C. Kazantsev is a member of an International Inter-IREM commission, which work on the multi-languages problem for children in the mathematical learning. Three meetings take place in Paris during the year, the first was on October 2. Last year, most of them were on visioconference.

11.3.4 Creation of media or tools for science outreach

• C. Kazantsev participated in the edition of the Teachers notebooks which explain and advise how to use the "La Grange Suitcases" (sets of mathematical games, problems and animations) destined for primary and secondary schools teachers as well as for the general public.
• C. Kazantsev participated in the creation of mathematical activities that can be autonomously used by schoolchildren of primary and secondary schools and by the general public.
• C. Kazantsev participated in the creation of a mathematical serious game that can be played by schoolchildren of secondary schools and by the general public. See www.la-grange-des-maths.fr/mission-exoplanetes/
• C. Kazantsev participated in the creation of a mathematical exposition on Johannes Kepler : "Kepler, les maths pour décrire le monde", in colaboration with Jean-Louis Hodeau, a cristallograph of the Neel Institut and CNRS (Grenoble, France). This exposition was visited on the fête de la science by schoolchildren of secondary schools and by the general public.
• C. Kazantsev had encadred a group of seven students of Télécom SudParis high school for a project named "Learn By Play". They created a game "Math'Venture" with ten mathematical challenges. See www.la-grange-des-maths.fr/mathventure

11.3.5 Interventions

• E. Blayo gave several outreach talks, in particular for middle school and high school students, and for more general audiences.
• Clémentine Prieur was invited to give a training at Ecole Thématique sur les Incertitudes en Calcul Scientifique (ETICS) 2021, Sept. 12-17, 2021, Erdeven (France).
• Clémentine Prieur was invited to give a training at the 8th edition of the research school organized by the CNRS research group EGRIN (Ecoulements Gravitaires et RIsques Naturels), June 29-July 02, 2020, Nouan-le-Fuzelier (reported to May, 27-28, 2021 as a virtual event).
• C. Kazantsev and E. Blayo are strongly involved in the creation of "La Grange des maths", a science popularization center that will be located in Varces (south of Grenoble), which will offer a huge variety of mathematical hands-on exhibits. See www.la-grange-des-maths.fr
• C. Kazantsev participated to the Fête de la Science with a mathematical exposition on Johannes Kepler : "Kepler, les maths pour décrire le monde" presented in the CNRS - Neel Institut.
• C. Kazantsev participated to the Fête de la Science with a presentation of the activities created by the association "La Grange des Maths".
• E. Arnaud participated to a training day for primary school teachers on critical thinking, oct. 2021
• E. Arnaud has given a seminar "(se) tromper avec les chiffres", at La fête de la sciences, oct. 2021

International journals

• 1 articleZ.Zineb Abidi, K.Khalid Minaoui, A.Anass El Aouni, A.Ayoub Tamim and H.Hicham Laanaya. An Efficient Detection of Moroccan Coastal Upwelling Based on Fusion of Chlorophyll-a and Sea Surface Temperature Images With a New Validation Index.IEEE Geoscience and Remote Sensing Letters188August 2021, 1322-1326
  HALDOI
• 2 articleF.Francis Auclair, L.Laurent Debreu, E.Emilie Duval, M.Margot Hilt, P.Patrick Marchesiello, E.Eric Blayo, F.Franck Dumas and Y.Yves Morel. Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean.Ocean Modelling168December 2021, 1-20
  HALDOIback to text
• 3 articleM.María Belén Heredia, C.Clémentine Prieur and N.Nicolas Eckert. Nonparametric estimation of aggregated Sobol' indices: application to a depth averaged snow avalanche model.International Journal of Reliability, Quality and Safety Engineering212August 2021, 107422:1-14
  HALDOIback to text
• 4 articleM.Matthieu Brachet and J.-P.Jean-Pierre Croisille. Spherical Shallow Water Waves Waves Simulation by a Cubed Sphere Finite Difference Solver.Quarterly Journal of the Royal Meteorological Society147735January 2021, 786-800
  HALDOIback to text
• 5 articleT.Théo Brivoal, G.Guillaume Samson, H.Hervé Giordani, R.Romain Bourdallé-Badie, F.Florian Lemarié and G.Gurvan Madec. Impact of the current feedback on kinetic energy over the North-East Atlantic from a coupled ocean/atmospheric boundary layer model.Ocean Science2021
  HALDOIback to text
• 6 articleA.Anass El Aouni. A hybrid identification and tracking of Lagrangian mesoscale eddies.Physics of Fluids333March 2021, 036604
  HALDOI
• 7 articleL.Laurent Gilquin, C.Clémentine Prieur, É.Élise Arnaud and H.Herve Monod. Iterative estimation of Sobol’ indices based on replicated designs.Computational and Applied Mathematics4018January 2021
  HALDOIback to text
• 8 articleA.Adrien Hirvoas, C.Clémentine Prieur, É.Élise Arnaud, F.Fabien Caleyron and M.Miguel Munoz Zuniga. Quantification and reduction of uncertainties in a wind turbine numerical model based on a global sensitivity analysis and a recursive Bayesian inference approach.International Journal for Numerical Methods in Engineering12210May 2021, 2528-2544
  HALDOIback to text
• 9 articleJ.-B.Jean-Bernard Lasserre, V.Victor Magron, S.Swann Marx and O.Olivier Zahm. Minimizing rational functions: a hierarchy of approximations via pushforward measures.SIAM Journal on Optimization313June 2021, 2285–2306
  HALDOI
• 10 articleF.Florian Le Guillou, N.Noé Lahaye, C.Clément Ubelmann, S.Sammy Metref, E.Emmanuel Cosme, A.Aurélien Ponte, J.Julien Le Sommer, E.Eric Blayo and A.Arthur Vidard. Joint Estimation of Balanced Motions and Internal Tides From Future Wide‐Swath Altimetry.Journal of Advances in Modeling Earth Systems1312December 2021, e2021MS002613:1-17
  HALDOIback to text
• 11 articleF.Florian Lemarié, G.Guillaume Samson, J.-L.Jean-Luc Redelsperger, H.Hervé Giordani, T.Théo Brivoal and G.Gurvan Madec. A simplified atmospheric boundary layer model for an improved representation of air-sea interactions in eddying oceanic models: implementation and first evaluation in NEMO (4.0).Geoscientific Model Development141January 2021, 543 - 572
  HALDOIback to text
• 12 articleL.Long Li, J.Jianwei Ma, F.-X.Francois-Xavier Le Dimet and A.Arthur Vidard. Assimilation of Images via Dictionary Learning-Based Sparsity Regularization Strategy: An Application for Retrieving Fluid Flows.IEEE Transactions on Geoscience and Remote SensingSeptember 2021, 1-20
  HALDOIback to text
• 13 articleP.Patrick Marchesiello, F.Francis Auclair, L.Laurent Debreu, J. C.James C. Mcwilliams, R.Rafael Almar, R.Rachid Benshila and F.Franck DUMAS. Tridimensional nonhydrostatic transient rip currents in a wave-resolving model.Ocean Modelling163July 2021, 101816
  HALDOIback to text
• 14 articleO.Olivier Marti, S.Sébastien Nguyen, P.Pascale Braconnot, S.Sophie Valcke, F.Florian Lemarié and E.Eric Blayo. A Schwarz iterative method to evaluate ocean–atmosphere coupling schemes: implementation and diagnostics in IPSL-CM6-SW-VLR.Geoscientific Model Development Discussions145May 2021, 2959 - 2975
  HALDOIback to text
• 15 articleC.Charles Pelletier, F.Florian Lemarié, E.Eric Blayo, M.-N.Marie-Noëlle Bouin and J.-L.Jean-Luc Redelsperger. Two-sided turbulent surface layer parameterizations for computing air-sea fluxes.Quarterly Journal of the Royal Meteorological Society147736April 2021, 1726-1751
  HALDOIback to text
• 16 articleS.Saman Razavi, A.Anthony Jakeman, A.Andrea Saltelli, C.Clémentine Prieur, B.Bertrand IOOSS, E.Emanuele Borgonovo, E.Elmar Plischke, S.Samuele Lo Piano, T.Takuya Iwanaga, W.William Becker, S.Stefano Tarantola, J. H.Joseph H.A. Guillaume, J.John Jakeman, H.Hoshin Gupta, N.Nicola Melillo, G.Giovanni Rabitti, V.Vincent Chabridon, Q.Qingyun Duan, X.Xifu Sun, S.Stefán Smith, R.Razi Sheikholeslami, N.Nasim Hosseini, M.Masoud Asadzadeh, A.Arnald Puy, S.Sergei Kucherenko and H.Holger Maier. The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support.Environmental Modelling and Software137March 2021, 104954
  HALDOIback to text
• 17 articleS.Saman Razavi, A. J.Anthony J. Jakeman, A.Andrea Saltelli, C.Clémentine Prieur, B.Bertrand Iooss, E.Emanuele Borgonovo, E.Elmar Plischke, S.Samuele Lo Piano, T.Takuya Iwanaga, W.William Becker, S.Stefano Tarantola, J. H.Joseph H.A. Guillaume, J.John Jakeman, H.Hoshin Gupta, N.Nicola Melillo, G.Giovanni Rabitti, V.Vincent Chabridon, Q.Qingyun Duan, X.Xifu Sun, S.Stefan Smith, R.Razi Sheikholeslami, N.Nasim Hosseini, M.Masoud Asadzadeh, A.Arnald Puy, S.Sergei Kucherenko and H. R.Holger R. Maier. The Future of Sensitivity Analysis: An Essential Discipline for Systems Modelling and Policy Making.Environmental Modelling and Software137March 2021, 1-22
  HALDOIback to text
• 18 articleS.Sophie Thery, C.Charles Pelletier, F.Florian Lemarié and E.Eric Blayo. Analysis of Schwarz Waveform Relaxation for the Coupled Ekman Boundary Layer Problem with Continuously Variable Coefficients.Numerical AlgorithmsJuly 2021
  HALDOIback to text
• 19 articleV.Victor Trappler, É.Élise Arnaud, A.Arthur Vidard and L.Laurent Debreu. Robust calibration of numerical models based on relative regret.Journal of Computational Physics426February 2021, 109952:1-19
  HALDOI
• 20 articleA.Achim Wirth and F.Florian Lemarié. Jarzynski equality and Crooks relation for local models of air-sea interaction.Earth System DynamicsApril 2021
  HALDOIback to text

Conferences without proceedings

• 21 inproceedingsE.Eric Blayo, F.Florian Lemarié, C.Charles Pelletier, S.Sophie Thery and S.Simon Clement. Improved coupling formulations and time integration strategies for ocean-atmosphere interactions.COUPLED 2021 - 9th International Conference on Coupled Problems in Science and EngineeringVirtual, ItalyJune 2021
  HAL
• 22 inproceedingsA.Anass El Aouni and H.Hassan Moustahfid. An Unsupervised Machine Learning Algorithm for the Identification and Tracking of Lagrangian Mesoscale Eddies.3rd NOAA Workshop on Leveraging Artificial Intelligence in Environmental SciencesSilver Spring MD, United StatesSeptember 2021, 1
  HAL
• 23 inproceedingsF.Florian Lemarié. Analysis of Ocean-Atmosphere Coupling from the Point of View of Domain Decomposition Methods.USNCCM16 2021 - 16th U.S. National Congress on Computational MechanicsChicago, United StatesJuly 2021
  HALback to textback to text
• 24 inproceedingsF.Florian Lemarié. Consistent subgrid scale modeling for oceanic climate models.IMPT 2021 - Ecole d'automne 2021 - Institut des Mathématiques pour la Planète Terre - Impacts morphologiques du changement climatiqueLyon, FranceNovember 2021
  HALback to textback to text
• 25 inproceedingsK.Katarina Radišić, E.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. Sensitivity Analysis of a Spatio-Temporal Hydrological Model for Pesticide Transfers.Rencontres MEXICO 2021Toulouse, FranceNovember 2021
  HALback to text
• 26 inproceedingsE.Emilie Rouzies, C.Claire Lauvernet, B.Bruno Sudret and A.Arthur Vidard. How can we quantify and reduce the uncertainty of a watershed-scale pesticide transfer model? A comparison of several approaches.UNCECOMP 2021 - 4th International Conference on Uncertainty Quantification in Computational Sciences and EngineeringAthens, GreeceJune 2021, 1-14
  HAL
• 27 inproceedingsE.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. Assimilating surface moisture satellite images into a coupled and spatialized water quality model: strategies and challenges.International EnKF workshop 2021Bergen, SwedenJune 2021, 1-17
  HALback to text
• 28 inproceedingsE.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. How can we quantify and reduce uncertainties of a catchment-scale pesticide transfer model? Application to the PESHMELBA model.Rencontres Mexico 2021Toulouse, FranceNovember 2021, 1-31
  HALback to text

Scientific books

• 29 bookS.Sébastien Da Veiga, F.Fabrice Gamboa, B.Bertrand Iooss and C.Clémentine Prieur. Basics and Trends in Sensitivity Analysis: Theory and Practice in R.SIAM2021, 1-16
  HALback to text

Doctoral dissertations and habilitation theses

• 30 thesisS.Sophie Thery. Numerical study of ocean-atmosphere coupling algorithms taking into account boundary layer parameterizations.Université Grenoble Alpes [2020-....]February 2021
  HALback to textback to text
• 31 thesisV.Victor Trappler. Parameter control in the presence of uncertainties.Université Grenoble Alpes [2020-....]June 2021
  HALback to textback to text

Reports & preprints

• 32 miscR.Ricardo Baptista, Y.Youssef Marzouk, R. E.Rebecca E. Morrison and O.Olivier Zahm. Learning non-Gaussian graphical models via Hessian scores and triangular transport.January 2022
  HALback to text
• 33 miscR.Rishabh Bhatt, L.Laurent Debreu and A.Arthur Vidard. Introducing time parallelisation within data assimilation using parareal method.January 2022
  HALback to text
• 34 miscD.Daniele Bigoni, Y.Youssef Marzouk, C.Clémentine Prieur and O.Olivier Zahm. Nonlinear dimension reduction for surrogate modeling using gradient information.February 2021
  HALback to text
• 35 miscM.Marie Billaud-Friess, A.Arthur Macherey, A.Anthony Nouy and C.Clémentine Prieur. A PAC algorithm in relative precision for bandit problem with costly sampling.February 2021
  HALback to text
• 36 miscS.Simon Clement, F.Florian Lemarié and E.Eric Blayo. Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients.January 2022
  HALback to text
• 37 miscT.Tiangang Cui, S.Sergey Dolgov and O.Olivier Zahm. Conditional Deep Inverse Rosenblatt Transports.January 2022
  HALback to text
• 38 miscT.Tiangang Cui and O.Olivier Zahm. Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems.March 2021
  HAL
• 39 miscR.Reda El Amri, C.Céline Helbert, M.Miguel Munoz Zuniga, C.Clémentine Prieur and D.Delphine Sinoquet. Set inversion under functional uncertainties with Gaussian ProcessRegression defined in the joint space of control and uncertain.2021
  HALback to text
• 40 miscP.Pierre Etoré, J. R.Jose R León and C.Clémentine Prieur. A probabilistic point of view for the exact or approximated computation of the solution to Kolmogorov hypoelliptic equations.September 2021
  HAL
• 41 miscA.Adrien Hirvoas, C.Clémentine Prieur, É.Élise Arnaud, F.Fabien Caleyron and M. M.Miguel Munoz Zuniga. Wind turbine quantification and reduction of uncertainties based on a data-driven data assimilation approach.December 2021
  HAL
• 42 miscP.Philomène Le Gall, A.-C.Anne-Catherine Favre, P.Philippe Naveau and C.Clémentine Prieur. Improved regional frequency analysis of rainfall data.January 2021
  HAL
• 43 reportO.Olivier Marti, S.Sébastien Nguyen, P.Pascale Braconnot, S.Sophie Valcke, F.Florian Lemarié and E.Eric Blayo. Diagnosing the ocean-atmosphere coupling schemes by using a mathematically consistent Schwarz iterative method.Research activities in Earth system modelling. Working Group on Numerical Experimentation. Report No. 51. WCRP Report No.4/2021. WMO, GenevaJuly 2021
  HALback to text
• 44 miscM.Matthieu Oliver, D.Didier Georges and C.Clémentine Prieur. Spatialized Epidemiological Forecasting applied to Covid-19 Pandemic at Departmental Scale in France.November 2021
  HALback to textback to text
• 45 reportO.Olivier Roustant, R.Rodolphe Le Riche, J.Josselin Garnier, D.David Ginsbourger, Y.Yves Deville, C.Céline Helbert, L.Luc Pronzato, C.Clémentine Prieur, F.Fabrice Gamboa, F.François Bachoc, J.Jeremy Rohmer, G.Guillaume Perrin, A.Amandine Marrel, G.Guillaume Damblin, A.Alain Gliere, D.Delphine Sinoquet, Y.Yann Richet, S.Sébastien Da Veiga and F.Frédéric Huguet. Chair in applied mathematics OQUAIDO Activity report.Mines Saint-Etienne; Ecole Centrale Lyon; BRGM (Bureau de recherches géologiques et minières); CEA; IFP Energies Nouvelles; Institut de Radioprotection et de Sûreté Nucléaire; Safran Tech; Storengy; CNRS; Université Grenoble - Alpes; Université Nice - Sophia Antipolis; Université Toulouse 3 (Paul Sabatier)April 2021
  HAL
• 46 miscE.Emilie Rouzies, C.Claire Lauvernet, B.Bruno Sudret and A.Arthur Vidard. How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model ? Application to the PESHMELBA model.January 2022
  HALback to text
• 47 miscO.Olivier Zahm, T.Tiangang Cui, K.Kody Law, A.Alessio Spantini and Y.Youssef Marzouk. Certified dimension reduction in nonlinear Bayesian inverse problems.March 2021
  HAL

Other scientific publications

• 48 inproceedings A.Anass El Aouni and A.Arthur Vidard. How well mesoscale eddies are represented in oceanic models? 2021 - ECMWF/OceanPredict workshop on Advances in Ocean Data Assimilation Shinfield Park, United Kingdom May 2021
  HAL
• 49 inproceedingsE.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. How to reduce uncertainties in a coupled and spatialized water quality model using data assimilation?vEGU21 - European Geosciences UnionVienne, AustriaApril 2021, 1
  HAL