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.
By Jing Xu, Zenglin Xu, Li Yi, Ruoxi Jiang, Yuan Qi
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
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: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: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