arXiv AI By Wenshuo Wang, Fan Zhang

Posterior-First Neural PDE Simulation: Inferring What Downstream Tasks Need from a Single Field

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Posterior-First Neural PDE Simulation proposes a new paradigm where downstream tasks dictate the minimal problem state to infer, and a posterior over that state conditions future predictions. The approach replaces traditional field-to-future predictors, which collapse distinct latent states, with a task-to-target-to-interface framework that preserves necessary ambiguity. Experiments on synthetic and PDEBench tasks show that posterior recovery improves rollout accuracy, reducing error by 59.4% of the direct-to-oracle gap.

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