arXiv：cs.LG· Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, Yuefan Deng·· 5 小时前AI 评分38
SCOPE：面向稀疏 PDE 推理的观测条件化全目标预测
SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference
AI 导读
SCOPE（Sparse-Context Observability-aware Predictive Embeddings）通过将全场上隐变量预测与物理重建耦合，从稀疏观测中恢复完整 PDE 场，并保持确定性单次推理。
正文
Authors:Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, Yuefan Deng
Abstract:Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. Diffusion-based PDE solvers address this problem through iterative sampling whereas neural operators provide deterministic one-pass predictions. We propose SCOPE (Sparse-Context Observability-aware Predictive Embeddings) to recover complete PDE fields from sparse observations by coupling full-field latent prediction with physical reconstruction. A shared decoder reconstructs fields from both predicted and complete-view representations so that representation learning is guided by both physical recovery and latent matching. We derive a quadratic risk decomposition at fixed teacher-decoder pairs showing why optimal latent prediction need not yield optimal field reconstruction. We also establish sufficient conditions for decoder improvements on complete inputs to transfer to recovery from partial observations. Experiments across five PDE settings show that SCOPE outperforms mask-aware neural operators on all ten forward and inverse tasks and achieves lower errors than those reported for diffusion-based solvers including DiffusionPDE and FunDPS. Decoder-only adaptation further improves recovery without retraining the backbone while retaining deterministic single-pass inference.
| Comments: | 34 pages, including supplementary material. Code: this https URL. Author affiliation updated. Updated future-work discussion |
| Subjects: | Machine Learning (cs.LG); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2609.36527 [cs.LG] |
| (or arXiv:2609.36527v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.36527 arXiv-issued DOI via DataCite |
Submission history
From: Ruichen Xu [view email]
[v1]
Tue, 29 Sep 2026 02:19:19 UTC (2,570 KB)
[v2]
Wed, 30 Sep 2026 16:45:35 UTC (2,570 KB)
[v3]
Thu, 1 Oct 2026 19:24:28 UTC (2,570 KB)
来源：arXiv：cs.LG · arxiv.org