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Bibliographic Details
Main Authors: Boesen, Tue, Haber, Eldad, Ascher, Uri Michael
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2211.14302
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author Boesen, Tue
Haber, Eldad
Ascher, Uri Michael
author_facet Boesen, Tue
Haber, Eldad
Ascher, Uri Michael
contents This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations on manifolds and implement related methods in residual neural networks, despite some fundamental scenario differences. Constraint or auxiliary information effects are incorporated through stabilization as well as projection methods, and we show when to use which method based on experiments involving simulations of multi-body pendulums and molecular dynamics scenarios. Several of our methods are easy to implement in existing code and have limited impact on training performance while giving significant boosts in terms of inference.
format Preprint
id arxiv_https___arxiv_org_abs_2211_14302
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Neural DAEs: Constrained neural networks
Boesen, Tue
Haber, Eldad
Ascher, Uri Michael
Machine Learning
Computational Physics
70H99, 34A09
This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations on manifolds and implement related methods in residual neural networks, despite some fundamental scenario differences. Constraint or auxiliary information effects are incorporated through stabilization as well as projection methods, and we show when to use which method based on experiments involving simulations of multi-body pendulums and molecular dynamics scenarios. Several of our methods are easy to implement in existing code and have limited impact on training performance while giving significant boosts in terms of inference.
title Neural DAEs: Constrained neural networks
topic Machine Learning
Computational Physics
70H99, 34A09
url https://arxiv.org/abs/2211.14302