Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields
Read the original on arXiv Machine Learning →Neural surrogates for forecasting physical fields from sparse, noisy sensors typically use a spatial window and a temporal history of past snapshots. This study compares the trade‑off between window size and history length against the Bayes‑optimal error, showing that for fields with local dynamics the optimal forecast relies mainly on distant sensors via spatial correlation. Experiments on Burgers flow and the chaotic Kuramoto‑Sivashinsky equation reveal that the benefit of additional snapshots depends on lead time and system stability, leading to design rules that size the window in correlation lengths and split input budgets between window and history based on forecast horizon.
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