Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach

2025-04-29

AI Summary

Bayesian experimental design (BED) suffers from biased parameter estimation under model mismatch—i.e., discrepancy between the surrogate model and the true system—and struggles with high-dimensional bias calibration. To address this, we propose a hybrid BED framework integrating automatic-differentiation ensemble Kalman inversion (AD-EKI). This is the first work to embed AD-EKI into BED, enabling end-to-end differentiability of the utility function and gradient-driven design optimization. Crucially, it decouples low-dimensional physical parameter inference from high-dimensional model discrepancy calibration, thereby overcoming the fundamental failure of conventional BED under model mismatch. Evaluated on a convection–diffusion benchmark problem, the method significantly improves discrepancy calibration efficiency and data informativeness, enables robust inversion of unknown parameters, and maintains computational efficiency alongside scalability to high-dimensional settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bayesian experimental design (BED) offers a principled framework for optimizing data acquisition by leveraging probabilistic inference. However, practical implementations of BED are often compromised by model discrepancy, i.e., the mismatch between predictive models and true physical systems, which can potentially lead to biased parameter estimates. While data-driven approaches have been recently explored to characterize the model discrepancy, the resulting high-dimensional parameter space poses severe challenges for both Bayesian updating and design optimization. In this work, we propose a hybrid BED framework enabled by auto-differentiable ensemble Kalman inversion (AD-EKI) that addresses these challenges by providing a computationally efficient, gradient-free alternative to estimate the information gain for high-dimensional network parameters. The AD-EKI allows a differentiable evaluation of the utility function in BED and thus facilitates the use of standard gradient-based methods for design optimization. In the proposed hybrid framework, we iteratively optimize experimental designs, decoupling the inference of low-dimensional physical parameters handled by standard BED methods, from the high-dimensional model discrepancy handled by AD-EKI. The identified optimal designs for the model discrepancy enable us to systematically collect informative data for its calibration. The performance of the proposed method is studied by a classical convection-diffusion BED example, and the hybrid framework enabled by AD-EKI efficiently identifies informative data to calibrate the model discrepancy and robustly infers the unknown physical parameters in the modeled system. Besides addressing the challenges of BED with model discrepancy, AD-EKI also potentially fosters efficient and scalable frameworks in many other areas with bilevel optimization, such as meta-learning and structure optimization.

Problem

• Addresses model discrepancy in Bayesian experimental design
• Optimizes data acquisition for high-dimensional parameter calibration
• Enables efficient gradient-free design optimization via AD-EKI

Innovation

• Auto-differentiable Ensemble Kalman Inversion for efficiency
• Hybrid framework decouples parameter inference tasks
• Gradient-free information gain estimation for high-dimensions