Interpretable learning of effective dynamics for multiscale systems
Emmanuel Menier Sebastian Kaltenbach Mouadh Yagoubi Marc Schoenauer Petros Koumoutsakos
The modeling and simulation of high-dimensional multiscale systems is a
critical challenge across all areas of science and engineering. It is broadly
believed that even with today's computer advances resolving all spatiotemporal
scales described by the governing equations remains a remote target. This
realization has prompted intense efforts to develop model order reduction
techniques. In recent years, techniques based on deep recurrent neural networks
have produced promising results for the modeling and simulation of complex
spatiotemporal systems and offer large flexibility in model development as they
can incorporate experimental and computational data. However, neural networks
lack interpretability, which limits their utility and generalizability across
complex systems. Here we propose a novel framework of Interpretable Learning
Effective Dynamics (iLED) that offers comparable accuracy to state-of-the-art
recurrent neural network-based approaches while providing the added benefit of
interpretability. The iLED framework is motivated by Mori-Zwanzig and Koopman
operator theory, which justifies the choice of the specific architecture. We
demonstrate the effectiveness of the proposed framework in simulations of three
benchmark multiscale systems. Our results show that the iLED framework can
generate accurate predictions and obtain interpretable dynamics, making it a
promising approach for solving high-dimensional multiscale systems.