OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators

2026-06-26

AI Summary

Traditional Shapley value computation is computationally prohibitive, and existing learnable explanation methods struggle with the non-uniform grids and irregular geometries commonly encountered in physical simulations. This work proposes OperatorSHAP—the first mesh-agnostic attribution method that extends Shapley values to function spaces. By integrating neural operator architectures with a learnable explainer, OperatorSHAP delivers consistent explanations across varying mesh resolutions without requiring model retraining. The method establishes a theoretical connection to the Aumann–Shapley value and demonstrates strong empirical alignment with discrete Shapley values across multiple grid resolutions. Consequently, it significantly enhances both the efficiency and generalization of model interpretability in physics-informed applications.

Abstract

Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis. Shapley values satisfy many desirable properties as an attribution method, but their computational cost during inference hinders their practical use. Current amortized explainers, such as FastSHAP, are limited to homogeneous inputs, which is problematic for physical applications where data often comes from irregular grids and geometries. We introduce OperatorSHAP, a grid-agnostic attribution method and training procedure that allows us to train FastSHAP-like explainers for neural operators. We establish a theoretical framework for attributions in function space, connecting to Aumann-Shapley values. We further show that OperatorSHAP's explanations are consistent with state-of-the-art discrete Shapley values across resolutions and transfer across grid sizes without retraining.

Problem

• Shapley values
• model interpretability
• neural operators
• irregular grids
• attribution methods

Innovation

• OperatorSHAP
• Neural Operators
• Shapley Values
• Grid-Agnostic Attribution
• Aumann-Shapley