Bayesian Adaptive Calibration and Optimal Design

TL;DR

This paper introduces a Bayesian adaptive experimental design method for calibrating computer models efficiently, leveraging Gaussian process models to maximize information gain and reduce the number of simulations needed.

Contribution

It proposes a novel batch-sequential algorithm that jointly estimates posterior parameters and optimal designs using a variational lower bound of expected information gain.

Findings

Outperforms existing methods on synthetic data

Reduces number of simulations for calibration

Effective on real-world calibration problems

Abstract

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current machine learning approaches, however, mostly rely on rerunning simulations over a fixed set of designs available in the observed data, potentially neglecting informative correlations across the design space and requiring a large amount of simulations. Instead, we consider the calibration process from the perspective of Bayesian adaptive experimental design and propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. At each round, the algorithm jointly estimates the parameters of the posterior distribution and optimal designs by maximising a variational lower bound of the expected information gain. The simulator is modelled as a sample from a Gaussian process, which allows us to correlate simulations and observed data with the unknown calibration parameters. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.