Enregistré dans:
Détails bibliographiques
Auteurs principaux: Long, Da, Zhe, Shandian, Williams, Samuel, Oliker, Leonid, Bai, Zhe
Format: Preprint
Publié: 2025
Sujets:
Accès en ligne:https://arxiv.org/abs/2503.11899
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866908546172452864
author Long, Da
Zhe, Shandian
Williams, Samuel
Oliker, Leonid
Bai, Zhe
author_facet Long, Da
Zhe, Shandian
Williams, Samuel
Oliker, Leonid
Bai, Zhe
contents Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales and the interplay of diverse physical processes, which manifest in PDEs through coupled, nonlinear terms that govern the evolution of multiple physical fields across scales. Neural operators have shown potential in short-term prediction of such complex spatio-temporal dynamics; however, achieving stable high-fidelity predictions and providing robust uncertainty quantification over extended time horizons remains an open and unsolved area of research. These limitations often lead to stability degradation with rapid error accumulation, particularly in long-term forecasting of systems characterized by multi-scale behaviors involving dynamics of different orders. To address these challenges, we propose an autoregressive Spatio-temporal Fourier Transformer (StFT), in which each transformer block is designed to learn the system dynamics at a distinct scale through a dual-path architecture that integrates frequency-domain and spatio-temporal representations. By leveraging a structured hierarchy of \ours blocks, the resulting model explicitly captures the underlying dynamics across both macro- and micro- spatial scales. Furthermore, a generative residual correction mechanism is introduced to learn a probabilistic refinement temporally while simultaneously quantifying prediction uncertainties, enhancing both the accuracy and reliability of long-term probabilistic forecasting. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.
format Preprint
id arxiv_https___arxiv_org_abs_2503_11899
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction
Long, Da
Zhe, Shandian
Williams, Samuel
Oliker, Leonid
Bai, Zhe
Machine Learning
Signal Processing
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales and the interplay of diverse physical processes, which manifest in PDEs through coupled, nonlinear terms that govern the evolution of multiple physical fields across scales. Neural operators have shown potential in short-term prediction of such complex spatio-temporal dynamics; however, achieving stable high-fidelity predictions and providing robust uncertainty quantification over extended time horizons remains an open and unsolved area of research. These limitations often lead to stability degradation with rapid error accumulation, particularly in long-term forecasting of systems characterized by multi-scale behaviors involving dynamics of different orders. To address these challenges, we propose an autoregressive Spatio-temporal Fourier Transformer (StFT), in which each transformer block is designed to learn the system dynamics at a distinct scale through a dual-path architecture that integrates frequency-domain and spatio-temporal representations. By leveraging a structured hierarchy of \ours blocks, the resulting model explicitly captures the underlying dynamics across both macro- and micro- spatial scales. Furthermore, a generative residual correction mechanism is introduced to learn a probabilistic refinement temporally while simultaneously quantifying prediction uncertainties, enhancing both the accuracy and reliability of long-term probabilistic forecasting. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.
title StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction
topic Machine Learning
Signal Processing
url https://arxiv.org/abs/2503.11899