Project CNRS IEA

Over the past years, designing efficient numerical methods for solving forward and inverse problems related to parameter-dependent evolution equations has become an active field in Model Order Reduction (MOR) community. Formerly, many effort has been put on finding suitable linear approximation methods in low-rank format in order to best represent the solution of such equations. However, it is now well understood that such approaches reach their limits e.g. for transport dominated equations. This is why more sophis- ticated architectures are required to efficiently address these problems, leading to nonlinear approximation methods. In this direction, recent approaches involving Neural Networks (NN) architectures trained with machine learning techniques have emerged. But the question of constructing such an approximation only using the equation and taking into account time-dependencies in the architecture is crucial, in particular when considering data assimilation problems. This project mainly concerns the study of dynamical nonlinear approximation, using NN, for the solving forward and inverse problems related to parameter-dependent evolution equations.

Keywords. Parameter-dependent evolution equations, forward and inverse problems, dynamical nonlinear approximation, data assimilation

Budget : 8k€

Duration : 2 years (2024-2025)

Consortium