Bayesian Adaptive Calibration and Optimal Design
This addresses the problem of costly simulation runs in physical sciences calibration, offering a more efficient approach for researchers and practitioners, though it is incremental as it builds on Bayesian and Gaussian process methods.
The paper tackles the inefficiency of calibrating computer models by proposing a Bayesian adaptive experimental design algorithm that selects maximally informative simulations in a batch-sequential process, achieving data efficiency and improved performance over existing methods in synthetic and real-data problems.
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.