arXiv：cs.LG· Ruige Kong·· 13 小时前
空间上下文还是记忆？为部分观测场神经代理模型确定输入规模
Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields
AI 导读
研究测量神经代理模型窗口与历史快照的权衡，对照贝叶斯最优误差。在除 KS 外的场中，八个快照随预测提前期增大而消除更小比例的单快照误差，KS 中则更大，该提前期反转在多种传感器密度、三种架构和二维域中持续存在。设计规则是窗口按关联长度确定，并按模型服务的提前期分配窗口与历史预算，Burgers 流中提前期 1 选的分割在提前期 8 时误差是最佳值的 13.5 倍。
正文
Abstract:Neural surrogates that forecast a physical field from sparse, noisy sensors read a window of nearby sensors and a history of past snapshots. Practitioners choose both by comparing fitted models with each other. Such comparisons cannot tell a model's shortfall from missing information. We measure the trade-off between window and history against the Bayes-optimal error of the same readings. An exact Gaussian analysis shows that noisy or sparse observation of a field with local dynamics makes the optimal forecast read distant sensors only through spatial correlation. On a forced linear field with a known optimum, trained models that read only the window come within 1% of it. We then train such models on viscous Burgers flow and the chaotic Kuramoto-Sivashinsky (KS) equation, with every deciding comparison fixed before any test evaluation. In every field except KS, eight snapshots remove a smaller fraction of the one-snapshot error as the lead time, the number of steps to the forecast target, grows. In KS, for windows up to one correlation length, they remove a larger fraction. This lead-time inversion persists across sensor densities, three architectures and a two-dimensional domain. It shrinks as damping lowers the Lyapunov exponent. Damping also removes the linear instability of KS. We therefore tie the inversion to instability and leave chaos and linear amplification unseparated. For surrogate design the results give two rules. Size the window in correlation lengths of the field. Split a fixed input budget between window and history for the lead time the model will serve, because the best split moves toward wider windows as the lead time grows. In Burgers flow the split chosen at lead time one ends with 13.5 times the best error at lead time eight.
| Comments: | 26 pages, 11 figures, 8 tables. Code: this https URL |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12723 [cs.LG] |
| (or arXiv:2610.12723v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12723 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ruige Kong [view email]
[v1]
Thu, 8 Oct 2026 21:04:45 UTC (699 KB)
来源：arXiv：cs.LG · arxiv.org