[2603.25025] System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting

Computer Science > Artificial Intelligence arXiv:2603.25025 (cs) [Submitted on 26 Mar 2026] Title:System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting Authors:Wenshuo Wang, Fan Zhang View a PDF of the paper titled System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting, by Wenshuo Wang and 1 other authors View PDF HTML (experimental) Abstract: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, ...