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

TL;DR

This paper introduces GPLaSDI, a hybrid deep-learning and Bayesian reduced-order-model that accelerates PDE solutions by up to 100,000 times while providing uncertainty quantification and maintaining high accuracy.

Contribution

It develops a novel autoencoder-based framework that learns latent space dynamics with uncertainty quantification, enabling fast and reliable physical simulations.

Findings

Achieves up to 100,000 times speed-up in simulations

Maintains less than 7% relative error on fluid mechanics problems

Incorporates uncertainty quantification and active learning

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.