Learning and Optimization with Bayesian Hybrid Models

TL;DR

This paper demonstrates that Bayesian hybrid models effectively combine physics-based and machine learning approaches to improve decision-making accuracy under uncertainty, especially with limited data.

Contribution

It introduces a Bayesian hybrid modeling framework that corrects systematic bias and applies it to ballistic firing, showing advantages over traditional models.

Findings

Bayesian hybrid models outperform pure machine learning in bias correction.

They require less data to achieve accurate predictions.

The approach improves decision-making under uncertainty.

Abstract

Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with less data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty.