A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems
The D2D framework treats predictive distributions directly instead of point states for forecasting dynamical systems. It uses kernel mean embeddings to compress input distributions into a neural format and mixture density networks to decode outputs back into probabilistic forecasts. This allows for recursive, uncertainty-aware multi-step forecasting without needing explicit ensemble simulations, proving that predictive distributions can be propagated effectively through neural models.