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

• URL: http://arxiv.org/abs/2312.01021v1
• Date: Sat, 2 Dec 2023 04:03:32 GMT
• Title: Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations
• Authors: Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, Jonathan L. Belof
• Abstract summary: We present Traditional, a hybrid deep-learning and Bayesian ROM.a. We trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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