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.
Neural operators enable fast PDE forecasting, but repeated predictions accumulate errors and fine-scale structures remain difficult to resolve. We introduce a frequency-decomposed finite-time flow-map...
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:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
arXiv:2607. 00197v1 Announce Type: new Abstract: Long-horizon multivariate time series forecasting (LTSF) remains challenging due to non-stationarity, regime shifts, and error accumulation.
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:2607. 09537v1 Announce Type: new Abstract: Time series forecasting requires models to capture diverse, often mutually exclusive, temporal dynamics, from smooth trend continuation to nonstationary drift and strict phase-aligned recurrence.
arXiv:2501. 04339v2 Announce Type: replace-cross Abstract: We introduce the Deep Convolutional Interpreter for Time Series (DCIts), a deep-learning architecture for nonlinear multivariate time series that provides sample-specific, locally interpretable descriptions of the underlying interaction structure.
arXiv:2509. 24122v3 Announce Type: replace Abstract: At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences?
arXiv:2606. 24969v1 Announce Type: new Abstract: While the quadratic sequence-length bottleneck of transformers has fueled a resurgence in recurrent models, effectively capturing complex dynamics requires architectures that balance efficient training with highly expressive latent states.
arXiv:2508. 05287v3 Announce Type: replace-cross Abstract: Existing time series foundation models (TSFMs), often based on transformer variants, lack adaptability to different sampling rates, struggle with generalization across varying context and target lengths, and are computationally inefficient.
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:2607. 08234v1 Announce Type: cross Abstract: Real-world time series exhibit complex dynamics characterized by multiple simultaneous temporal patterns: short-term fluctuations, periodic seasonal cycles, long-term trends, and irregular abrupt changes.