Pith. sign in

REVIEW 1 cited by

GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2206.05183 v4 pith:4Y4SJXU5 submitted 2022-06-10 cs.LG cs.NAmath.DSmath.NAphysics.data-anstat.ML

classification cs.LGcs.NAmath.DSmath.NAphysics.data-anstat.ML
keywords dynamicsmethodsnonlinearautoencodersgd-vaesgeometriclearnlearning
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric flow regularization in latent spaces for smooth dynamics with the efficient variations of curvature

    math.NA 2025-06 conditional novelty 5.0 of 10

    Curvature-flow-regularized latent spaces improve mean out-of-distribution errors for Burger's equation relative to a plain autoencoder, but the flows are heuristic and the evidence is limited.

Pith tools