Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations

Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, Jonathan L. Belof
12/2/2023
cs.CEcs.LGmath.NA

Official code: llnl/GPLaSDI (37 stars, MIT, last commit 2026-02-14).

Abstract

Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. These equations are interpolated with Gaussian Processes, allowing for uncertainty quantification and active learning, even with limited access to the FOM solver. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.

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Code Implementations(1)

llnl/GPLaSDIOfficial
MIT

Gaussian process-based interpretable latent space dynamics identification through deep autoencoder

377C, ShellJul 30, 20238 months agoMIT
math-physicspde

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Cite this paper

@article{bonneville2023datadriven,
  title  = {Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations},
  author = {Christophe Bonneville and Youngsoo Choi and Debojyoti Ghosh and Jonathan L. Belof},
  year   = {2023},
  eprint = {2312.01021},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2312.01021v1}
}

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