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The modeling and simulation of high-dimensional multiscale systems is acritical challenge across all areas of science and engineering. It is broadlybelieved that even with today's computer advances resolving all spatiotemporalscales described by the governing equations remains a remote target. Thisrealization has prompted intense efforts to develop model order reductiontechniques. In recent years, techniques based on deep recurrent neural networkshave produced promising results for the modeling and simulation of complexspatiotemporal systems and offer large flexibility in model development as theycan incorporate experimental and computational data. However, neural networkslack interpretability, which limits their utility and generalizability acrosscomplex systems. Here we propose a novel framework of Interpretable LearningEffective Dynamics (iLED) that offers comparable accuracy to state-of-the-artrecurrent neural network-based approaches while providing the added benefit ofinterpretability. The iLED framework is motivated by Mori-Zwanzig and Koopmanoperator theory, which justifies the choice of the specific architecture. Wedemonstrate the effectiveness of the proposed framework in simulations of threebenchmark multiscale systems. Our results show that the iLED framework cangenerate accurate predictions and obtain interpretable dynamics, making it apromising approach for solving high-dimensional multiscale systems.

Interpretable learning of effective dynamics for multiscale systems