Disentangled Multi-Fidelity Deep Bayesian Active Learning

TL;DR

This paper introduces D-MFDAL, a deep Bayesian active learning framework for multi-fidelity simulations, improving prediction accuracy and efficiency over existing methods in high-dimensional PDE surrogate modeling.

Contribution

It proposes a novel disentangled deep Bayesian approach that effectively models multiple fidelity levels without hierarchical constraints, enhancing scalability and accuracy.

Findings

Outperforms state-of-the-art methods in benchmark PDE tasks

Achieves higher prediction accuracy with fewer samples

Demonstrates scalability to high-dimensional data

Abstract

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency.