mlsanityData to 7 Oct 2026

Bi-fidelity Variational Auto-encoder for Uncertainty Quantification

arXiv 2305.16530 ↗First posted 25 May 2023stat.ML cs.LG cs.NAcited by 8

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Abstract (arXiv)

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 that 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 BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 22 of its 62 references that are in the map. First posted on arXiv 25 May 2023.

Builds on

22 of 62 references.

References · 22

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
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  11. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  12. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
10 more
  1. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 127
  2. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  3. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  4. 2020Solving inverse problems using conditional invertible neural networkscited by 37
  5. 2017Adversarial Generation of Natural Languagecited by 33
  6. 2020On transfer learning of neural networks using bi-fidelity data for uncertainty propagationcited by 26
  7. 2021Neural Network Training Using ℓ1-Regularization and Bi-fidelity Datacited by 16
  8. 2021VAE Approximation Error: ELBO and Exponential Familiescited by 12
  9. 2023Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equationscited by 8
  10. 2022PCENet: High Dimensional Surrogate Modeling for Learning Uncertaintycited by 5

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Cited by year

Citing papers per year: 2024: 4; 2025: 4.

8 papers.

  1. 2024At the Dawn of Generative AI Era: A Tutorial-cum-Survey on New Frontiers in 6G Wireless Intelligencecited by 25
  2. 2024A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systemscited by 19
  3. 2025Bifidelity Parameter Estimation Using Conditional Diffusion Modelscited by 7
  4. 2024Sparse L1-Autoencoders for Scientific Data Compressioncited by 4
  5. 2024Graph Laplacian-based Bayesian Multi-fidelity Modelingcited by 1
  6. 2025LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian processcited by 1
  7. 2025Stochastic Subspace Descent Accelerated via Bi-fidelity Line Searchcited by 0
  8. 2025Multi-fidelity aerodynamic data fusion by autoencoder transfer learningcited by 0