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Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems

arXiv 2012.03448 ↗First posted 7 Dec 2020cs.LG cs.AI cs.SYcited by 50

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Abstract (arXiv)

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Dec 2020.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 5; 2024: 9; 2025: 20; 2026: 12.

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