Active Learning of Model Discrepancy with Bayesian Experimental Design

2025-02-07

AI Summary

Digital twin models commonly suffer from modeling bias; existing data-driven approaches are constrained by empirical data collection and struggle to efficiently learn high-dimensional biases. While Bayesian experimental design (BED) actively selects informative samples, it is highly susceptible to bias-induced performance degradation. This paper proposes the first sequential active learning framework that couples BED with bias learning. We introduce an ensemble-based approximation of information gain to overcome the failure of conventional BED under bias, and develop a differentiable architecture compatible with both automatic differentiation and classical numerical solvers. Evaluated on benchmark convection–diffusion equations, our method significantly improves accuracy and robustness in high-dimensional bias modeling. It establishes a novel paradigm for digital twin model calibration.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.

Problem

• Active learning of model discrepancy
• Bayesian experimental design optimization
• High-dimensional model discrepancy handling

Innovation

• Active learning via Bayesian Experimental Design.
• Iterative model discrepancy learning approach.
• Ensemble-based information gain approximation.