Physics-Informed Koopman Network
This addresses the data efficiency issue for researchers and practitioners in dynamical systems modeling, though it is incremental as it builds on existing physics-informed neural network methods.
The authors tackled the problem of large data requirements for neural networks representing Koopman operators by proposing a physics-informed architecture that imposes physical laws via soft constraints during training, resulting in reduced data needs while maintaining high effectiveness in approximating Koopman eigenfunctions.
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.