Active Learning with Fully Bayesian Neural Networks for Discontinuous and Nonstationary Data

TL;DR

This paper explores the use of Fully Bayesian Neural Networks with advanced sampling techniques as surrogate models for active learning in physical sciences, especially for systems with discontinuities and non-stationarities, demonstrating their effectiveness in small data regimes.

Contribution

It introduces the application of Fully Bayesian Neural Networks with No-U-Turn Sampler for active learning, addressing limitations of Gaussian Processes in complex physical systems.

Findings

FBNNs provide reliable predictive distributions for active learning.

FBNNs outperform Gaussian Processes on discontinuous and non-stationary test functions.

Effective in small data, low-dimensional physical science problems.

Abstract

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key component of this approach is a probabilistic surrogate model, typically a Gaussian Process (GP), which approximates an unknown functional relationship between control parameters and a target property. However, conventional GPs often struggle when applied to systems with discontinuities and non-stationarities, prompting the exploration of alternative models. This limitation becomes particularly relevant in physical science problems, which are often characterized by abrupt transitions between different system states and rapid changes in physical property behavior. Fully Bayesian Neural Networks (FBNNs) serve as a promising substitute, treating all neural network weights probabilistically and leveraging advanced Markov Chain Monte Carlo techniques for direct sampling from the posterior distribution. This approach enables FBNNs to provide reliable predictive distributions, crucial for making informed decisions under uncertainty in the active learning setting. Although traditionally considered too computationally expensive for 'big data' applications, many physical sciences problems involve small amounts of data in relatively low-dimensional parameter spaces. Here, we assess the suitability and performance of FBNNs with the No-U-Turn Sampler for active learning tasks in the 'small data' regime, highlighting their potential to enhance predictive accuracy and reliability on test functions relevant to problems in physical sciences.