A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes
type: Item
instance of: scholarly article
title: A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes
zbMATH Open document ID: 1498.65150
DOI: 10.4171/RLM/943
author: Francesco Regazzoni
author: Stefano Pagani
author: Alessandro Cosenza
author: Alessandro Lombardi
author: Alfio Quarteroni
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2022-02-15T00:00:00Z
review text: In this article, the authors introduce a multi-fidelity approach to estimate an unknown parameter based on Physics-Informed Neural Networks (PINNs). The authors developed two different multi-fidelity approaches: MPINN-v1 and MPINN-v2. The first one is based on a parameter-independent low-fidelity solution which acts only as the parameter's initial guess, to estimate the solution of the PDE. The second approach is based on a parameter-dependent low-fidelity solution with a training procedure designed to minimize simultaneously the distance between the solution of PDE and the data, the distance between the solution of PDE and the low-fidelity approximation for the same parameter value, and the residual of the equation. Numerical tests were performed for an advection-diffusion-reaction equation, and the Bueno-Orovio ionic nonlinear model describing the ionic dynamics of cardiac cells, focusing on the case of few noisy measurements. Finally, they conclude that the multi-fidelity approach is promising for solving realistic optimization problems involving noisy measurements and complex multiscale and multiphysics phenomena.
reviewed by: N. Barani Balan
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 68T07
Mathematics Subject Classification ID: 49M41
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 92C37
zbMATH DE Number: 7473888
zbMATH Keywords: physics-informed neural network
zbMATH Keywords: multifidelity
zbMATH Keywords: machine learning
zbMATH Keywords: partial differential equations
zbMATH Keywords: optimization
describes a project that uses: TensorFlow
describes a project that uses: SciPy
describes a project that uses: PINNsNTK
describes a project that uses: Keras
describes a project that uses: Adam
describes a project that uses: GitHub
MaRDI profile type: Publication
Wikidata QID: Q115211930
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full work available at URL: https://doi.org/10.4171/rlm/943
OpenAlex ID: W4200500918
description: scientific article; zbMATH DE number 7473888