# Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance

arXiv: https://arxiv.org/abs/2601.16425 · HTML: https://mlsanity.com/paper/2601.16425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 57 of its 154 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## Builds on (most cited first, 30 of 57)

- [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)

## Abstract (arXiv)

Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates experimental planning with probabilistic inference, the selection of utility functions in BED is a long-standing and active topic, where different criteria emphasize different notions of information. Although Kullback--Leibler (KL) divergence has been one of the most common choices, recent studies have proposed Wasserstein distance as an alternative. In this work, we first employ a toy example to illustrate an issue of Wasserstein distance - the value of Wasserstein distance of a fixed-shape posterior depends on the relative position of its main mass within the support and can exhibit false rewards unrelated to information gain, especially with a non-informative prior (e.g., uniform distribution). We then further provide a systematic comparison between these two criteria through a classical source inversion problem in the BED literature, revealing that the KL divergence tends to lead to faster convergence in the absence of model discrepancy, while Wasserstein metrics provide more robust sequential BED results if model discrepancy is non-negligible. These findings clarify the trade-offs between KL divergence and Wasserstein metrics for the utility function and provide guidelines for selecting suitable criteria in practical BED applications.