Should We Simultaneously Calibrate Multiple Computer Models?

TL;DR

This paper introduces a probabilistic neural network framework for simultaneous calibration of multiple computer models, addressing multi-response data and model-form errors, with potential improvements in predictive accuracy.

Contribution

It develops a novel neural network-based approach for calibrating multiple models at once, considering multi-response data and variable calibration parameters.

Findings

Improves predictive accuracy in model calibration.

Prone to non-identifiability in high-dimensional spaces.

Effective on analytic and engineering problems.

Abstract

In an increasing number of applications designers have access to multiple computer models which typically have different levels of fidelity and cost. Traditionally, designers calibrate these models one at a time against some high-fidelity data (e.g., experiments). In this paper, we question this tradition and assess the potential of calibrating multiple computer models at the same time. To this end, we develop a probabilistic framework that is founded on customized neural networks (NNs) that are designed to calibrate an arbitrary number of computer models. In our approach, we (1) consider the fact that most computer models are multi-response and that the number and nature of calibration parameters may change across the models, and (2) learn a unique probability distribution for each calibration parameter of each computer model, (3) develop a loss function that enables our NN to emulate all data sources while calibrating the computer models, and (4) aim to learn a visualizable latent space where model-form errors can be identified. We test the performance of our approach on analytic and engineering problems to understand the potential advantages and pitfalls in simultaneous calibration of multiple computer models. Our method can improve predictive accuracy, however, it is prone to non-identifiability issues in higher-dimensional input spaces that are normally constrained by underlying physics.