Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting

arXiv cs.LG / 4/27/2026

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Key Points

The paper addresses the operational need to explain neural-network predictions on dynamic physical fields, motivated by autoregressive weather forecasting use cases.
It shows that standard gradient-based explanation averaging (e.g., SmoothGrad-style pointwise averaging) can fail on dynamic physical fields because input perturbations produce geometric misalignment rather than stationary amplitude noise, leading to blurred attributions.
The authors propose WassersteinGrad, which replaces pointwise averaging with an entropic Wasserstein barycenter to compute a geometric consensus across perturbed attribution maps.
Experiments on regional weather data using a meteorologist-validated neural model indicate that WassersteinGrad improves explainability compared with gradient-based baselines in both single-step and autoregressive forecasting settings.

Abstract

As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our work is motivated by the explanations of autoregressive neural predictions on dynamic physical fields, as in weather forecasting. Gradient-based feature attribution methods are widely used to explain the predictions on such data, in particular due to their scalability to high-dimensional inputs. It is also interesting to remark that gradient-based techniques such as SmoothGrad are now standard on images to robustify the explanations using pointwise averages of the attribution maps obtained from several noised inputs. Our goal is to efficiently adapt this aggregation strategy to dynamic physical fields. To do so, our first contribution is to identify a fundamental failure mode when averaging perturbed attribution maps on dynamic physical fields: stochastic input perturbations do not induce stationary amplitude noise in attribution maps, but instead cause a geometric displacement of the attributions. Consequently, pointwise averaging blurs these spatially misaligned features. To tackle this issue, we introduce WassersteinGrad, which extracts a geometric consensus of perturbed attribution maps by computing their entropic Wasserstein barycenter. The results, obtained on regional weather data and a meteorologist-validated neural model, demonstrate promising explainability properties of WassersteinGrad over gradient-based baselines across both single-step and autoregressive forecasting settings.