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

arXiv: https://arxiv.org/abs/2601.22860 · HTML: https://mlsanity.com/paper/2601.22860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Exact posterior distributions of wide Bayesian neural networks](https://mlsanity.com/paper/2006.10541/) (2020)
- [Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.05320/) (2023)
- [BlendedNet: A Blended Wing Body Aircraft Dataset and Surrogate Model for Aerodynamic Predictions](https://mlsanity.com/paper/2509.07209/) (2025)
- [Inexpensive High Fidelity Melt Pool Models in Additive Manufacturing Using Generative Deep Diffusion](https://mlsanity.com/paper/2311.16168/) (2023)
- [Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems](https://mlsanity.com/paper/2503.02041/) (2025)

## Abstract (arXiv)

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, 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.