Bayesian Model Calibration with Integrated Discrepancy: Addressing Inexact Dislocation Dynamics Models

TL;DR

This paper introduces a new Bayesian calibration method that integrates discrepancy modeling directly into simulators using Gaussian processes, improving calibration accuracy for complex physical models like dislocation dynamics.

Contribution

The paper presents a novel Bayesian calibration approach that incorporates integrated discrepancy GPs within simulators, contrasting with traditional methods that treat discrepancy separately.

Findings

Applied to Molecular Dynamics and Dislocation Dynamics simulations.

Demonstrated improved calibration accuracy over traditional KOH method.

Provided a framework for when to use integrated discrepancy calibration.

Abstract

In this work, a novel approach to Bayesian model calibration routines is developed which reinterprets the traditional definition of model discrepancy as defined by Kennedy and O'Hagan (KOH). The novelty lies in the integration of $\delta_\theta(x_i)$ GPs within the simulator, which is approximated as a GP surrogate model to ensure computational tractability. This approach assumes that the utilized simulator sufficiently predicts observed trends when calibrated with respect to the application domain, and that all model-form errors can be attributed to uncertainty in the input parameters. In contrast, the KOH method assumes discrepancy to be inherently decoupled from the simulator, acting as a 'catch-all' for various sources of model error. The new method is applied to Molecular Dynamics observations of the critical stress to drive dislocation dipoles, and equivalent predictions using a Discrete Dislocation Dynamics simulator whose coarse-grained physical interpretation of the underlying physical mechanisms requires calibration against MD observations. We present an overview of similar state-aware calibration routines; differentiate the provided approach through redefining the commonly used discrepancy Gaussian process and benchmark against KOH. A philosophical argument as to when application of the proposed method is appropriate is provided, and future directions for expanding upon this methodology are proposed.