Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes

• URL: http://arxiv.org/abs/2305.00094v1
• Date: Fri, 28 Apr 2023 21:11:13 GMT
• Title: Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes
• Authors: Francesco Regazzoni and Stefano Pagani and Matteo Salvador and Luca Dede' and Alfio Quarteroni
• Abstract summary: Latent Dynamics Network (LDNet) is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems. LDNets are lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes.
• Score: 2.3694122563610924
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to yield predictions through the numerical approximation of high-dimensional systems of differential equations, thus calling for large-scale parallel computing platforms and requiring large computational costs. Data-driven approaches, instead, enable the description of systems evolution in low-dimensional latent spaces, by leveraging dimensionality reduction and deep learning algorithms. We propose a novel architecture, named Latent Dynamics Network (LDNet), which is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems, thus predicting the time evolution of space-dependent fields in response to external inputs. Unlike popular approaches, in which the latent representation of the solution manifold is learned by means of auto-encoders that map a high-dimensional discretization of the system state into itself, LDNets automatically discover a low-dimensional manifold while learning the latent dynamics, without ever operating in the high-dimensional space. Furthermore, LDNets are meshless algorithms that do not reconstruct the output on a predetermined grid of points, but rather at any point of the domain, thus enabling weight-sharing across query-points. These features make LDNets lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes. We validate our method on several test cases and we show that, for a challenging highly-nonlinear problem, LDNets outperform state-of-the-art methods in terms of accuracy (normalized error 5 times smaller), by employing a dramatically smaller number of trainable parameters (more than 10 times fewer).

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