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A spatially adaptive neural operator (SANO), which replaces this spatially shared parameterization with a spatially continuous field of location-dependent operator parameters, which consistently outperforms competitive neural-operator, hypernetwork-based, and physics-informed baselines.
A geometry-aware incremental neural operator (GeoIncNO) for stable long-horizon PDE prediction and a mean--fluctuation decoupled reconstruction mechanism, where stable mean structures and dynamic fluctuations are fused separately, and phase correction is applied only to the zero-mean fluctuation component.
Experiments show that HERO consistently improves long-horizon accuracy, stable rollout length, and out-of-distribution robustness at no inference-time cost, indicating that history-enriched relative supervision is effective for stabilizing long-horizon autoregressive prediction.
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