Towards Model Discovery Using Domain Decomposition and PINNs

TL;DR

This paper compares domain decomposition-enhanced PINNs and FBPINNs for learning parameters in complex ODE systems, demonstrating FBPINNs' superior performance especially with limited or quasi-stationary data.

Contribution

It introduces and evaluates FBPINNs as an improvement over vanilla PINNs for model discovery in complex dynamical systems.

Findings

FBPINNs outperform vanilla PINNs in accuracy.

Fewer data points needed for FBPINNs to learn effectively.

Robustness of FBPINNs with noisy and limited data.

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.