Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems
This addresses the need for practical uncertainty-driven active learning in industrial simulations where computational efficiency and reliability are critical, representing a strong specific gain rather than a foundational breakthrough.
The paper tackles the problem of limited scalability and poor reliability in neural networks for uncertainty quantification in large-scale physical systems, proposing the Bayesian Interpolating Neural Network (B-INN) which achieves speeds 20 to 10,000 times faster than Bayesian neural networks and Gaussian processes with robust uncertainty estimation.
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.