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

As AI becomes integral to high-stakes domains like weather forecasting, understanding why a neural network makes a particular prediction is no longer optional—it's a strict operational requirement. Gradient-based feature attribution methods, such as SmoothGrad, are widely used to explain predictions on high-dimensional inputs like weather maps. However, these techniques average attribution maps from noised inputs pointwise, which works well for static images but fails for dynamic physical fields where perturbations cause geometric displacement of attributions, not stationary amplitude noise.

To address this, researchers from Météo-France and Université de Toulouse developed WassersteinGrad. Instead of pointwise averaging, WassersteinGrad computes the entropic Wasserstein barycenter of perturbed attribution maps. This approach extracts a geometric consensus that preserves the spatial alignment of features, avoiding the blurring that plagues traditional methods. The team validated WassersteinGrad on regional weather data using a meteorologist-approved neural model, demonstrating superior explainability in both single-step and autoregressive forecasting scenarios. This work, published on arXiv (2604.22580), marks a significant step toward reliable AI explanations in dynamic physical systems.