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This content will become publicly available on September 1, 2026

Title: GD-VAEs: Geometric dynamic variational autoencoders for learning nonlinear dynamics and dimension reductions
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.  more » « less
Award ID(s):
2306101 1616353
PAR ID:
10611625
Author(s) / Creator(s):
;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of Computational Physics
Volume:
537
Issue:
C
ISSN:
0021-9991
Page Range / eLocation ID:
114127
Subject(s) / Keyword(s):
Machine Learning Data-Driven Modeling Variational Autoencoders Dimension Reduction Dynamical Systems Scientific Computation
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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