Simultaneous Calibration of an Arbitrary Number of Multiresponse Computer Models

Abstract In an increasing number of applications, designers have access to multiple computer models that 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) before using them for downstream design tasks. In this article, we question this tradition and assess the potential of jointly calibrating an arbitrary number of computer models that simulate the same underlying physical phenomenon. To this end, we develop a probabilistic framework that is founded on customized neural networks (NNs) that are devised to calibrate multiple computer models. In our approach, we (1) consider the fact that most computer models are multiresponse and that the number and nature of calibration parameters may change across the models, (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 visualizable latent spaces where model-form errors can be probed. 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 nonidentifiability issues in high-dimension input and output spaces if knowledge from the underlying physics is not leveraged during training or architecture design.