Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Bi-fidelity variational auto-encoder for uncertainty quantification

Journal Article · · Computer Methods in Applied Mechanics and Engineering
 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [1];  [1]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
  3. Northern Arizona Univ., Flagstaff, AZ (United States)
+ Show Author Affiliations

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. Here, 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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
US Air Force Office of Scientific Research (AFOSR); USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231; SC0023346
OSTI ID:
2474863
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 421; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (35)

Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression journal June 2015
Multi-fidelity non-intrusive polynomial chaos based on regression journal June 2016
A generalized probabilistic learning approach for multi-fidelity uncertainty quantification in complex physical simulations journal October 2022
Kernel principal component analysis-based Gaussian process regression modelling for high-dimensional reliability analysis journal December 2020
Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders journal March 2022
Multi-output local Gaussian process regression: Applications to uncertainty quantification journal July 2012
A weighted -minimization approach for sparse polynomial chaos expansions journal June 2014
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies journal January 2015
A low-rank control variate for multilevel Monte Carlo simulation of high-dimensional uncertain systems journal July 2017
Basis adaptive sample efficient polynomial chaos (BASE-PC) journal October 2018
Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction journal September 2018
Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification journal August 2018
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification journal December 2018
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems journal March 2019
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data journal October 2019
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders journal November 2019
Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks journal February 2020
A generalized approximate control variate framework for multifidelity uncertainty quantification journal May 2020
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder journal February 2022
Neural network training using ℓ1-regularization and bi-fidelity data journal June 2022
Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations journal February 2024
Graph Laplacian-based spectral multi-fidelity modeling journal October 2023
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders journal March 2021
Variational Inference: A Review for Statisticians journal July 2016
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs journal July 2016
Predicting the output from a complex computer code when fast approximations are available journal March 2000
Rethinking the Inception Architecture for Computer Vision conference June 2016
Action-Conditioned 3D Human Motion Synthesis with Transformer VAE conference October 2021
Bayesian calibration of computer models journal August 2001
Accurate Uncertainty Quantification Using Inaccurate Computational Models journal January 2009
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment journal January 2004
Generative adversarial networks journal October 2020
Kernel Optimization for Low-Rank Multifidelity Algorithms journal January 2021
On Transfer Learning of Neural Networks Using Bi-Fidelity data for Uncertainty Propagation journal January 2020
Adversarial Generation of Natural Language conference January 2017

Similar Records

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Generative modeling
Multi-fidelity
Transfer learning
Uncertainty quantification
Variational auto-encoder