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

arXiv: https://arxiv.org/abs/2504.20319 · HTML: https://mlsanity.com/paper/2504.20319/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 154 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 30 of 56)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models](https://mlsanity.com/paper/1703.07370/) (2017)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Tighter expected generalization error bounds via Wasserstein distance](https://mlsanity.com/paper/2101.09315/) (2021)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2110.15335/) (2021)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Automatic structured variational inference](https://mlsanity.com/paper/2002.00643/) (2020)

## Built on by (most cited first, 2 of 2)

- [Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling](https://mlsanity.com/paper/2602.17089/) (2026)
- [Active Learning for Communication Structure Optimization in LLM-Based Multi-Agent Systems](https://mlsanity.com/paper/2605.05703/) (2026)

## Abstract (arXiv)

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.