Bi-fidelity variational auto-encoder for uncertainty quantification

Nuojin Cheng, Osman Asif Malik, Subhayan De, Stephen Becker, Alireza Doostan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. This model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space which is integrated within the VAE's probabilistic encoder–decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that the BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

Original languageEnglish (US)
Article number116793
JournalComputer Methods in Applied Mechanics and Engineering
Volume421
DOIs
StatePublished - Mar 1 2024
Externally publishedYes

Keywords

  • Generative modeling
  • Multi-fidelity
  • Transfer learning
  • Uncertainty quantification
  • Variational auto-encoder

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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