Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields
Neural surrogates that forecast a physical field from sparse, noisy sensors read a window of nearby sensors and a history of past snapshots.
ProofPaper ↗
Key points
- We measure the trade-off between window and history against the Bayes-optimal error of the same readings.
- An exact Gaussian analysis shows that noisy or sparse observation of a field with local dynamics makes the optimal forecast read distant sensors only through spatial correlation.
- On a forced linear field with a known optimum, trained models that read only the window come within 1% of it.
- We then train such models on viscous Burgers flow and the chaotic Kuramoto-Sivashinsky (KS) equation, with every deciding comparison fixed before any test evaluation.
Sources (1)
- [1]Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed FieldsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 09:04 PM
Neural surrogates that forecast a physical field from sparse, noisy sensors read a window of nearby sensors and a history of past snapshots.
We measure the trade-off between window and history against the Bayes-optimal error of the same readings.
Extractive summary: sentences quoted from the sources.
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