FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Models

This work presents a novel graph neural network (GNN) architecture, the Feature-specific Interpretable Graph Neural Network (FIGNN), designed to enhance the interpretability of deep learning surrogate models defined on unstructured grids in scientific applications. Traditional GNNs often obscure the distinct spatial influences of di ff erent features in multivariate prediction tasks. FIGNN addresses this limitation by introducing a feature-specific pooling strategy, which enables independent attribution of spatial importance for each predicted variable. Additionally, a mask-based regularization term is incorporated into the training objective to explicitly encourage alignment between interpretabil-ity and predictive error, promoting localized attribution of model performance. The method is evaluated for surrogate modeling of two physically distinct systems: the SPEEDY atmospheric circulation model and the backward-facing step (BFS) fluid dynamics benchmark. Results demonstrate that FIGNN achieves competitive predictive performance while revealing physically meaningful spatial patterns unique to each feature. Analysis of rollout stability, feature-wise error budgets, and spatial mask overlays confirm the utility of FIGNN as a general-purpose framework for interpretable surrogate modeling in complex physical domains. Keywords: Graph Neural Networks, Interpretability, Top-K Pooling, Surrogate Modeling, Scientific Machine Learning 1. Introduction Graph Neural Networks (GNNs) have become increasingly prominent in modeling systems governed by partial di ff erential equations (PDEs) [1, 2, 3, 4, 5, 6].