SimPINNs: Simulation-Driven Physics-Informed Neural Networks for Enhanced Performance in Nonlinear Inverse Problems

TL;DR

SimPINNs introduces a hybrid physics-informed neural network approach that combines observed and simulated data to improve the accuracy and robustness of solving nonlinear inverse problems with lower-dimensional unknowns.

Contribution

The paper presents a novel hybrid loss function for PINNs that enhances performance in nonlinear inverse problems by integrating simulated physical data.

Findings

Outperforms standard PINNs in accuracy and robustness

Effective in problems with nonlinear forward models

Applicable to low-dimensional inverse problems

Abstract

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the underlying forward model demonstrates pronounced nonlinear behaviour, and where the dimensionality of the unknown parameter space is substantially smaller than that of the observations. Our proposed method builds upon physics-informed neural networks (PINNs) trained with a hybrid loss function that combines observed data with simulated data generated by a known (approximate) physical model. Experimental results on an orbit restitution problem demonstrate that our approach surpasses the performance of standard PINNs, providing improved accuracy and robustness.