System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911545244516352 |
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| author | Wang, Wenshuo Zhang, Fan |
| author_facet | Wang, Wenshuo Zhang, Fan |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25025 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting Wang, Wenshuo Zhang, Fan Artificial Intelligence 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). |
| title | System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2603.25025 |