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

• URL: http://arxiv.org/abs/2601.22860v1
• Date: Fri, 30 Jan 2026 11:38:42 GMT
• Title: Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems
• Authors: Chanwook Park, Brian Kim, Jiachen Guo, Wing Kam Liu,
• Abstract summary: This paper proposes a scalable and reliable Bayesian surrogate model, termed the Bayesian Interpolating Neural Network (B-INN)<n>B-INN combines high-order theory with tensor decomposition and alternating direction algorithm to enable effective dimensionality reduction without compromising predictive accuracy.<n> Numerical experiments demonstrate that B-INNs can be from 20 times to 10,000 times faster with a robust uncertainty estimation.
• Score: 0.8593015118377854
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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