Physics-Informed Koopman Network

TL;DR

This paper introduces a physics-informed neural network architecture for Koopman operator approximation that reduces data requirements while accurately capturing system dynamics by embedding physical laws during training.

Contribution

The novel architecture integrates physics-informed constraints into Koopman neural networks, decreasing data needs and improving eigenfunction approximation accuracy.

Findings

Reduces training data requirements significantly.

Maintains high accuracy in Koopman eigenfunction approximation.

Demonstrates effectiveness on nonlinear dynamical systems.

Abstract

Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate arbitrarily complex functions. However, despite their great potential, they typically require large training data-sets either from measurements of a real system or from high-fidelity simulations. In this work, we propose a novel architecture inspired by physics-informed neural networks, which leverage automatic differentiation to impose the underlying physical laws via soft penalty constraints during model training. We demonstrate that it not only reduces the need of large training data-sets, but also maintains high effectiveness in approximating Koopman eigenfunctions.