Inverse Problems for Shallow-Water Equations solved by Physics-Informed Machine Learning methods - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2024

Inverse Problems for Shallow-Water Equations solved by Physics-Informed Machine Learning methods

Résumé

Faced with the socio-economic challenges of flood forecasting, in a context of climate change, multi-scale modeling approaches that take advantage of the maximum amount of information available are needed to enable accurate and rapid flood forecasts. In this context, the objective of this work is to develop a Physics-Informed Machine Learning method to efficiently perform flood models calibration, which is crucial to ensure accurate forecasts. More precisely, an approach aiming at inferring a spatially-distributed friction coefficient (Manning-Strickler coefficient) from data with a Physics-Informed Neural Network (idea introduced by Lagaris et al. [1] and further developed by Raissi et al. [2]) is proposed. The method consists in considering for the loss function a physical model term corresponding to the 2D Shallow-Water Equations residual and a data discrepancy term. Data are generated with the reference software DassFlow1 and refer to observations of the free surface height and mass flow rate at various locations and times in the computational domain. The PINN parameters and the spatially-distributed friction parameter are then optimized so that the weighted sum of the physical residual term and the data discrepancy term are minimized. To tackle multi-scale issues, a multiresolution strategy is employed on the friction parameter, thus allowing to initialize the optimization with a coarse friction resolution and refining it iteratively throughout the training for regularization purposes. This work is aimed to be published in Boulenc et al. [3]. To illustrate the efficiency of the method and its sensitivity to the friction parameter dimension, two river hydraulic modeling test cases will be discussed. Overall, the proposed method appears efficient and robust. Moreover, it is simple to implement (non-intrusive) compared to more traditional Variational Data Assimilation approaches (Monnier [4]), making it a viable strategy to further enhance for rapid flood forecasts. [1] I.E. Lagaris, A. Likas, and D.I. Fotiadis. Artificial neural networks for solving ordinary and partial differential equations. IEEE transactions on neural networks, 9(5):987–1000, 1998. [2] M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378:686–707, 2019. [3] H. Boulenc, J. Monnier, P.-A. Garambois, and R. Bouclier. Physics-Informed Neural Net- works for high-dimensional data assimilation: formalism and illustration on Shallow-Water Equations. Pre-publication, in prep. to be submitted spring 2024. [4] J. Monnier. Data Assimilation. Inverse Problems, Assimilation, Control, Learning. Lectures notes, November 2021.
Fichier non déposé

Dates et versions

hal-04618150 , version 1 (20-06-2024)

Identifiants

  • HAL Id : hal-04618150 , version 1

Citer

Hugo Boulenc, Robin Bouclier, Pierre-André Garambois, Jerome Monnier. Inverse Problems for Shallow-Water Equations solved by Physics-Informed Machine Learning methods. ECCOMAS 2024 - 9th European Congress on Computational Methods in Applied Sciences and Engineering, Jun 2024, Lisbonne, Portugal. ⟨hal-04618150⟩
0 Consultations
0 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More