Inference in the presence of model-form uncertainties: Leveraging a prediction-oriented approach to improve uncertainty characterization

TL;DR

This paper explores a prediction-oriented inference approach to better characterize uncertainties in complex physics-based models, especially under model misspecification, demonstrating improved calibration over traditional Bayesian methods.

Contribution

It applies prediction-oriented inference to calibrate model-form uncertainties in physics-based models, addressing challenges of high-dimensional data and computational expense.

Findings

Prediction-oriented inference improves uncertainty calibration.

Method effectively calibrates model-form uncertainties.

Approach is applicable to complex scientific models.

Abstract

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and machine learning communities have developed prediction-oriented inference approaches that provide better calibrated uncertainties and adapt to the level of misspecification present. However, these approaches have yet to be demonstrated in the context of complex scientific applications where phenomena of interest are governed by physics-based models. Such settings often involve single realizations of high-dimensional spatio-temporal data and nonlinear, computationally expensive parameter-to-observable maps. This work investigates variational prediction-oriented inference in problems exhibiting these relevant features; namely, we consider a polynomial model and a contaminant transport problem governed by advection-diffusion equations. The prediction-oriented loss is formulated as the log-predictive probability of the calibration data. We study the effects of increasing misspecification and noise, and we assess approximations of the predictive density using Monte Carlo sampling and component-wise kernel density estimation. A novel aspect of this work is applying prediction-oriented inference to the calibration of model-form uncertainty (MFU) representations, which are embedded physics-based modifications to the governing equations that aim to reduce (but rarely eliminate) model misspecification. The computational results demonstrate that prediction-oriented frameworks can provide better uncertainty characterizations in comparison to standard inference while also being amenable to the calibration of MFU representations.