Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting
Existing gradient-based attribution methods suffer from blurred attribution maps in dynamic physical fields—such as numerical weather prediction—due to geometric displacements, undermining their reliability for interpretation. This work proposes WassersteinGrad, an attribution aggregation framework grounded in entropy-regularized Wasserstein barycenters, which aligns attribution maps generated from multiple perturbations via optimal transport, thereby overcoming the limitations of conventional pointwise averaging. WassersteinGrad reveals, for the first time, that attribution discrepancies primarily stem from geometric shifts rather than amplitude noise, enabling the construction of geometrically consistent attribution consensus. Evaluated on regional meteorological data using an autoregressive neural weather forecasting model validated by meteorologists, WassersteinGrad consistently outperforms existing gradient-based baselines in both single-step and multi-step forecasts, yielding significantly sharper and more stable explanations.