Amortized Shapley Interactions for Neural Operators

Explaining model predictions can increase trust in AI systems and provide valuable insights to developers. Feature-based attribution methods, such as Shapley values, are a popular approach to model interpretability. In the physical sciences, however, model inputs often represent continuous domains rather than discrete features. Additionally, their mesh-based discretizations may vary between samples, making fast amortized explanations difficult. Infinite-player Aumann–Shapley values have recently been proposed as an alternative for such continuous inputs, but the existing framework is limited to additive attributions and therefore cannot capture interactions between input regions. In this work, we propose *OperatorSHAP-IQ*, which extends the Aumann–Shapley framework to feature interactions. We further introduce an amortization scheme that enables efficient inference of interaction maps and show how different classes of partial differential equations exhibit different levels of interactions.