arXiv cs.AI· Wenshuo Wang, Fan Zhang·· 13 小时前AI 评分31
后验优先的神经 PDE 模拟：从单一观测场推断下游任务所需状态
Posterior-First Neural PDE Simulation: Inferring What Downstream Tasks Need from a Single Field
AI 导读
研究者提出“后验优先”神经 PDE 模拟范式，先由声明的下游任务确定需推断的最小任务充分问题状态，再用该状态的后验条件化 rollout 与下游查询。在 metadata-hidden 的 PDEBench 任务上，后验恢复将汇总 rollout nRMSE 从 0.175 降至 0.132，弥合了 59.4% 的 direct-to-oracle 差距，且该增益在潜扩散骨干下依然保持。
正文 · 原文
Abstract:Neural PDE simulators often receive only a single observed field at deployment. In this setting, a field-to-future predictor can collapse distinct latent problem states into the same deterministic interface, losing the ambiguity needed for reliable rollout and downstream decisions. We propose posterior-first neural PDE simulation, a task-to-target-to-interface paradigm: the declared downstream tasks determine the minimal task-sufficient problem state to infer, and the posterior over that state conditions the rollout and downstream queries. This posterior can be supplied by amortized posterior estimators, including simulation-based inference with learned summaries; our contribution is the target, the interface, and their theory. We show that Bayes downstream values factor through this posterior, proper scoring rules on refinement labels identify it as their population-risk minimizer, and deterministic collapse incurs an ambiguity barrier whenever the true posterior is non-Dirac. Synthetic exact-ambiguity experiments show that point-versus-posterior gaps track the predicted barrier. On metadata-hidden PDEBench tasks, posterior recovery reduces pooled rollout nRMSE from 0.175 to 0.132, closing 59.4% of the direct-to-oracle gap. Matched controls attribute the gains to task-aligned targeting and posterior deployment, and the gains persist with a latent-diffusion backbone. These results suggest that single-observation neural PDE simulation should be posterior-first rather than monolithic field-to-future prediction.
| Comments: | Accepted at NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.03247 [cs.LG] |
| (or arXiv:2605.03247v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.03247 arXiv-issued DOI via DataCite |
Submission history
From: Wenshuo Wang [view email]
[v1]
Tue, 5 May 2026 00:37:01 UTC (199 KB)
[v2]
Tue, 27 Oct 2026 12:03:14 UTC (195 KB)
来源：arXiv cs.AI · arxiv.org