提出SAKE方法，低成本高效选择物理模拟的上下文窗口。
System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting
- 基于系统特征锚点生成候选集，再进行关键点感知筛选。
- 在8个PDEBench任务中达到67.8%精确率与91.7%近似率。
- 适合需要低开销、高精度的物理场预测场景使用。
自回归神经偏微分方程（PDE）模拟器通过有限历史逐步预测物理场演化，但低成本上下文窗口选择仍缺乏明确方法。现有时间序列预测中的窗口选择方法包括全量验证、直接低成本搜索和系统理论记忆估计，但或成本高、或鲁棒性差，或与下游滚动预测性能不一致。本文将固定窗口自回归神经PDE模拟器的显式上下文窗口选择形式化为独立的低成本算法问题，提出两阶段方法System-Anchored Knee Estimation (SAKE)：首先从具有物理解释性的系统锚点中识别少量结构化候选集，然后在此集内执行膝点感知的下游选择。在所有八个PDEBench数据集上，采用共享的 $L\in\{1,\dots,16\}$ 协议评估，SAKE是预算匹配下表现最强的低成本选择器，实现67.8%精确率、91.7%近似率、6.1%平均违规@膝点，且成本比为0.051（节省94.9%搜索开销）。
原文摘要 · Abstract (English)
Autoregressive neural PDE simulators predict the evolution of physical fields one step at a time from a finite history, but low-cost context-window selection for such simulators remains an unformalized problem. Existing approaches to context-window selection in time-series forecasting include exhaustive validation, direct low-cost search, and system-theoretic memory estimation, but they are either expensive, brittle, or not directly aligned with downstream rollout performance. We formalize explicit context-window selection for fixed-window autoregressive neural PDE simulators as an independent low-cost algorithmic problem, and propose \textbf{System-Anchored Knee Estimation (SAKE)}, a two-stage method that first identifies a small structured candidate set from physically interpretable system anchors and then performs knee-aware downstream selection within it. Across all eight PDEBench families evaluated under the shared \(L\in\{1,\dots,16\}\) protocol, SAKE is the strongest overall matched-budget low-cost selector among the evaluated methods, achieving 67.8\% Exact, 91.7\% Within-1, 6.1\% mean regret@knee, and a cost ratio of 0.051 (94.9\% normalized search-cost savings).
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