发表机构
Stony Brook University; University of California, Davis; TikTok; PayPal; New York University; Northeastern University（石溪大学; 加州大学戴维斯分校; TikTok; PayPal; 纽约大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对稀疏观测恢复完整物理场问题，提出SCOPE方法，结合全场潜在预测与物理重建，在五个PDE任务上优于现有神经算子和扩散求解器，且支持仅解码器适应。
AI 中文摘要
从稀疏观测中恢复完整的物理场具有挑战性，因为测量可能无法唯一确定潜在状态。基于扩散的PDE求解器通过迭代采样解决此问题，而神经算子则提供确定性的单次预测。我们提出SCOPE（稀疏上下文可观测性感知预测嵌入），通过将全场潜在预测与物理重建相结合，从稀疏观测中恢复完整的PDE场。共享解码器从预测和完整视图表示中重建场，使得表示学习同时受到物理恢复和潜在匹配的指导。我们推导了固定教师-解码器对下的二次风险分解，表明最优潜在预测不一定产生最优场重建。我们还建立了完整输入上解码器改进转移到部分观测恢复的充分条件。在五个PDE设置上的实验表明，SCOPE在所有十个前向和逆任务中优于掩码感知神经算子，并且误差低于扩散型求解器（包括DiffusionPDE和FunDPS）报告的误差。仅解码器适应进一步改善恢复，无需重新训练骨干网络，同时保持确定性的单次推理。
英文摘要
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.
Comments34 pages, including supplementary material. Code: https://github.com/ru1ch3n/SCOPE. Author affiliation updated. Updated future-work discussion
