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

arXiv: https://arxiv.org/abs/2603.25025 · HTML: https://mlsanity.com/paper/2603.25025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
- [On the Benefits of Memory for Modeling Time-Dependent PDEs](https://mlsanity.com/paper/2409.02313/) (2024)
- [SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2403.19507/) (2024)
- [Lag Selection for Univariate Time Series Forecasting using Deep Learning: An Empirical Study](https://mlsanity.com/paper/2405.11237/) (2024)

## Built on by (most cited first, 1 of 1)

- [Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields](https://mlsanity.com/paper/2610.12723/) (2026)

## Abstract (arXiv)

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 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∈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).