arXiv Machine Learning By Nicholas Tan Jerome, Fangnian Wang

Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems

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The paper investigates why transferring relational structure learned from abundant forward-simulation data fails for inverse problems, despite theoretical expectations. It demonstrates that dynamics‑learned graphs, such as those from Neural Relational Inference, can worsen performance by over 100% compared to a task‑optimised attention baseline, and that this failure persists across multiple evidence lines. The authors formalise the gap as an approximation‑error issue and propose a lightweight transferability test based on Jaccard similarity to predict successful transfer.

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arXiv AI
Oct 28

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

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.

By Wenshuo Wang, Fan Zhang