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

Dimensions overall score 3.0

• A novel algorithmic approach for low-cost context window selection in autoregressive neural PDE simulators. 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.problem 35%
  Evidencepartial

  A novel algorithmic approach for low-cost context window selection in autoregressive neural PDE simulators. 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.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• 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.method 35%
  Evidencepartial

  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.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• ScienceToStartup currently rates this 3.0/10 on the public viability pass. 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).result 35%
  Evidencepartial

  ScienceToStartup currently rates this 3.0/10 on the public viability pass. 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).

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• PDE Forecasting moved forward this cycle; last verified April 2026. Public score 3.0/10.why now 35%
  Evidencepartial

  PDE Forecasting moved forward this cycle; last verified April 2026. Public score 3.0/10.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial