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F$^3$NO is a frequency‑decomposed finite‑time flow‑map neural operator that uses low‑frequency features to guide the refinement of high‑frequency information through cross‑scale conditioning within each layer. The model predicts future states directly for specified times and adjusts the contributions of its two branches based on the prediction interval. Experiments on five PDE benchmarks show that F$^3$NO outperforms autoregressive and direct‑prediction baselines, and ablation studies reveal that frequency‑decomposed refinement improves accuracy with fewer parameters while segmentation benefits vary with spatial resolution and dynamical regime.
arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
ReAl: Refine neural operators via aligning dynamical flow introduces a model‑agnostic plug‑in that enhances pretrained PDE surrogates by adding a refinement stage with a conditional flow‑matching model to recover missing high‑frequency structures, and an alignment stage that generates multiple trajectories and uses trajectory‑level rewards to stabilize long‑horizon predictions. The method improves high‑frequency fidelity, forecasting accuracy, and long‑horizon stability across diverse surrogate architectures and PDE tasks.
arXiv:2607. 19404v1 Announce Type: cross Abstract: Multivariate time series encode structural patterns that unfold across multiple temporal scales, yet most forecasting backbones treat learned representations as transient byproducts of prediction, leaving the organizational geometry of these patterns underexploited.
arXiv:2605. 25413v3 Announce Type: replace-cross Abstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs).
arXiv:2610.19552v1 Announce Type: new Abstract: Foundation models for dynamical systems can forecast unseen partial differential equations (PDEs), ordinary differential equations (ODEs), and time ser...