Bi-fidelity Variational Auto-encoder for Uncertainty Quantification
arXiv:2305.16530 · doi:10.1016/j.cma.2024.116793
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 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.
References in corpus (23)
- Auto-Encoding Variational Bayes
- Denoising Diffusion Probabilistic Models
- Variational Inference: A Review for Statisticians
- The information bottleneck method
- Score-Based Generative Modeling through Stochastic Differential Equations
- Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
- Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
- Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
- Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
- Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
- Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy
- Compressive Sampling of Polynomial Chaos Expansions: Convergence Analysis and Sampling Strategies
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- A weighted L1-minimization approach for sparse polynomial chaos expansions
- Coherence Motivated Sampling and Convergence Analysis of Least-Squares Polynomial Chaos Regression
- Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
- A Generalized Approximate Control Variate Framework for Multifidelity Uncertainty Quantification
- Solving inverse problems using conditional invertible neural networks
- A Low-rank Control Variate for Multilevel Monte Carlo Simulation of High-dimensional Uncertain Systems
- Basis Adaptive Sample Efficient Polynomial Chaos (BASE-PC)
- Neural Network Training Using -Regularization and Bi-fidelity Data
- PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty
- Kernel optimization for Low-Rank Multi-Fidelity Algorithms