الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Xu, R., Wang, S., Wan, F., Qiu, J., Gao, W., Zhang, J., Pang, L., Shwartz-Ziv, R., Mehrotra, P., LeCun, Y., & Deng, Y. (2026). SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference. https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference
MLA 9
Xu, Ruichen, et al. "SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference." https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference.
شيكاغو (المؤلف–التاريخ)
Xu, Ruichen, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, and Yuefan Deng. 2026. "SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference." https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference.
هارفارد
Xu, R., Wang, S., Wan, F., Qiu, J., Gao, W., Zhang, J., Pang, L., Shwartz-Ziv, R., Mehrotra, P., LeCun, Y. and Deng, Y. (2026) 'SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference', Available at: https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference.
فانكوفر
Xu R, Wang S, Wan F, Qiu J, Gao W, Zhang J, et al. SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference. https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference
IEEE
R. Xu, S. Wang, F. Wan, J. Qiu, W. Gao, J. Zhang, L. Pang, R. Shwartz-Ziv, P. Mehrotra, Y. LeCun, and Y. Deng, "SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference," https://omanscience.com/ar/articles/scope-observation-conditioned-full-target-prediction-for-sparse-pde-inference.