Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines

Abstract

The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series representation through retaining only the most important basis terms. In this work, we present a novel sparse Bayesian learning technique for obtaining sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine model and is trained using Variational Inference. The methodology shows great potential in high-dimensional data-driven settings using relatively few data points and achieves user-controlled sparse levels that are comparable to other methods such as compressive sensing. The proposed approach is illustrated on two numerical examples, a synthetic response function that is explored for validation purposes and a low-carbon steel plate with random Young's modulus and random loading, which is modeled by stochastic finite element with 38 input random variables.

arXiv commentSubmitted to Journal of Computational Physics

References in corpus (10)

• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Variational Relevance Vector Machines
• Compressive Sampling of Polynomial Chaos Expansions: Convergence Analysis and Sampling Strategies
• Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (2000)
• A weighted L1-minimization approach for sparse polynomial chaos expansions
• A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions
• Compressive sensing adaptation for polynomial chaos expansions
• Reduced Wiener Chaos representation of random fields via basis adaptation and projection
• Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

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• Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
• Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes