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.
By Fan Wu, Cheng Jing, Kookjin Lee
arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
By Jiaquan Zhang, Shuxu Chen, Haifan Meng, Yi Lu, Zhihan Lyu, Fan Mo, Wei Dong, Yang Yang, Chaoning Zhang
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.
By Jing Xu, Zenglin Xu, Li Yi, Ruoxi Jiang, Yuan Qi
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.
By Xingsheng Chen, Deyu Yi, Siu-Ming Yiu
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).
By Jiaquan Zhang, Caiyan Qin, Haoyu Bian, Libin Cai, Yi Lu, Chaoning Zhang, Wei Dong, Yuanfang Guo, Yang Yang, Heng Tao Shen
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...
By Jeffrey B. Lai, John Quinn, Anthony Bao, William Gilpin
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.
By Haroon Gharwi, Yue Dai, Kai Shu
arXiv:2610. 05337v2 Announce Type: replace-cross Abstract: We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural operators typically treat them only as input values.
By Chenhao Si, Ming Yan
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.
By Qitai Tan, Ruiwen Gu, Yilin Su, Mo Li, Xu Lin, Xiao-Ping Zhang
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?
By Hongbo Liu, Jia Xu
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.
By Klaus Schertler, Xiomara Runge, Andrea Ceni, David Kappel, Claudio Gallicchio
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.
By Domjan Baric, Davor Horvatic