arXiv Machine Learning By Tianlin Yang, Hailiang Du, Louis Aslett

A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems

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A new distribution-to-distribution (D2D) neural probabilistic forecasting framework is introduced, using kernel mean embeddings to encode input distributions and mixture density networks to parameterise output distributions. The framework allows recursive multi-step forecasting directly in distributional form, avoiding the need for explicit ensemble simulations. Demonstrated on the Lorenz63 system, the D2D model captures complex distributional evolution and achieves skillful probabilistic forecasts comparable to a perfect-model benchmark.

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