Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems

TL;DR

The paper introduces B-INN, a scalable Bayesian neural network model that efficiently handles large-scale physical system data with reliable uncertainty quantification, outperforming traditional models in speed and robustness.

Contribution

It presents B-INN, a novel Bayesian surrogate model combining interpolation, tensor decomposition, and efficient inference, suitable for large-scale industrial applications.

Findings

B-INN achieves 20x to 10,000x faster inference than existing models.

The function space of B-INN is a subset of Gaussian processes.

B-INN provides robust uncertainty estimates in large-scale simulations.

Abstract

Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a single high-fidelity simulation may require days or weeks of computation and produce data volumes on the order of gigabytes, they quickly become impractical. This paper proposes a scalable and reliable Bayesian surrogate model, termed the Bayesian Interpolating Neural Network (B-INN). The B-INN combines high-order interpolation theory with tensor decomposition and alternating direction algorithm to enable effective dimensionality reduction without compromising predictive accuracy. We theoretically show that the function space of a B-INN is a subset of that of Gaussian processes, while its Bayesian inference exhibits linear complexity, $\mathcal{O}(N)$, with respect to the number of training samples. Numerical experiments demonstrate that B-INNs can be from 20 times to 10,000 times faster with a robust uncertainty estimation compared to Bayesian neural networks and Gaussian processes. These capabilities make B-INN a practical foundation for uncertainty-driven active learning in large-scale industrial simulations, where computational efficiency and robust uncertainty calibration are paramount.