Towards Model Discovery Using Domain Decomposition and PINNs

Tirtho S. Saha; Alexander Heinlein; Cordula Reisch

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arXiv · 2410.01599

Towards Model Discovery Using Domain Decomposition and PINNs

Tirtho S. Saha·Alexander Heinlein·Cordula Reisch

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Abstract

We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.

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Tirtho S. Saha, Alexander Heinlein, Cordula Reisch. 2024-10-02. Towards Model Discovery Using Domain Decomposition and PINNs. https://arxiv.org/abs/2410.01599

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