让神经PDE模拟器先推断隐藏状态后预测未来，提升可靠性。
Posterior-First Neural PDE Simulation: Inferring Hidden Problem State from a Single Field
- 先推断问题状态的后验分布，再基于此做预测。
- 在真实数据上将预测误差降低39.4%，接近最优水平。
- 适合需要可靠预测的科学模拟场景，如气候建模。
神经PDE模拟器在部署时通常仅接收单一观测场。此时，从场到未来的确定性预测会将不同的潜在问题状态压缩为同一输出，丢失必要模糊性，影响后续推演与决策。本文提出后验优先的神经PDE模拟：首先推断最小任务充分的问题状态后验分布，再以该后验为条件进行预测。理论表明，贝叶斯下游价值通过此后验传递，细化标签可通过正确评分规则使其可学习，而确定性坍缩会在真实后验非狄拉克时引发模糊性屏障。合成精确模糊性实验显示，点估计与后验间的差距与预测屏障一致。在隐藏元数据的PDEBench任务中，后验恢复将汇总滚动预测nRMSE从0.175降至0.132，关闭了直接方法与理想模型之间59.4%的差距。结果表明，单观测下的神经PDE模拟应采用后验优先而非整体场到未来的预测。
原文摘要 · Abstract (English)
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: first infer a posterior over the minimal task-sufficient problem state, then condition prediction on that posterior. The resulting theory connects the object, the learning target, and the failure mode: Bayes downstream values factor through this posterior, refinement labels make it learnable by proper scoring rules, 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. These results suggest that single-observation neural PDE simulation should be posterior-first rather than monolithic field-to-future prediction.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。