Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Francesco Regazzoni (), Stefano Pagani, Matteo Salvador, Luca Dede’ and Alfio Quarteroni
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Francesco Regazzoni: Politecnico di Milano
Stefano Pagani: Politecnico di Milano
Matteo Salvador: Politecnico di Milano
Luca Dede’: Politecnico di Milano
Alfio Quarteroni: Politecnico di Milano

Nature Communications, 2024, vol. 15, issue 1, 1-16

Abstract: Abstract Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equations, thus demanding extensive computational resources. In contrast, data-driven approaches leverage deep learning algorithms to describe system evolution in low-dimensional spaces. We introduce an architecture, termed Latent Dynamics Network, capable of uncovering low-dimensional intrinsic dynamics in potentially non-Markovian systems. Latent Dynamics Networks automatically discover a low-dimensional manifold while learning the system dynamics, eliminating the need for training an auto-encoder and avoiding operations in the high-dimensional space. They predict the evolution, even in time-extrapolation scenarios, of space-dependent fields without relying on predetermined grids, thus enabling weight-sharing across query-points. Lightweight and easy-to-train, Latent Dynamics Networks demonstrate superior accuracy (normalized error 5 times smaller) in highly-nonlinear problems with significantly fewer trainable parameters (more than 10 times fewer) compared to state-of-the-art methods.

Date: 2024
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DOI: 10.1038/s41467-024-45323-x

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