Knowledge-informed generative adversarial network for functional calibration of computer models

Abstract

Functional model calibration considers the input dependency of model parameters by explicitly considering them as functional calibration parameters. In this study, a novel knowledge-informed generative adversarial network (KI-GAN) is proposed for the functional calibration of computer models under uncertainty. The proposed KI-GAN leverages the superior distribution learning ability of generative models for uncertainty quantification of model parameters and uses prior knowledge to inform generative model training by formulating a knowledge-based loss function that can easily incorporate different types of physical and expert knowledge of the computer model and its parameters. Two experiments are presented to demonstrate the effectiveness of the proposed KI-GAN for calibrating the functional model parameters under various scenarios. The results indicate that the proposed KI-GAN can effectively encode various types of prior knowledge on the computer model and its parameters, such as partial differential equation constraints and derivative constraints, which can significantly improve the parameter estimation accuracy and reduce estimation uncertainty. Furthermore, with appropriate constraints applied, the proposed KI-GAN can estimate model parameters with reasonable accuracy even under sparse and noisy observations and quantify the underlying uncertainties. Finally, the trained generators can accurately infer the probabilistic distributions of unobserved model outputs without running the computer model.