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Spatially heterogeneous partial differential equations (PDEs) exhibit location-dependent dynamics arising from variations in geometry and physical coefficients. Existing neural operators improve localized modeling through multiscale features, attention mechanisms, or domain decomposition, yet their update rules often r...
A budget-aware framework that systematically orchestrates when and what to teach and integrates a solvability-aware teacher gate to dictate the teacher model and a score-guided turn selection mechanism to decide what informative turns to retain is proposed.
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.
Multi-view clustering aims to utilize information from multiple feature representations to uncover underlying data structures. Most existing methods emphasize learning a consensus representation by enforcing consistency across views. However, those structures that cannot be directly incorporated into the clustering spa...
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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