Autoregression-Free Neural Operators for Time-Dependent PDEs
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911725987561472 |
|---|---|
| author | Zhang, Jiaquan Qin, Caiyan Bian, Haoyu Cai, Libin Lu, Yi Zhang, Chaoning Dong, Wei Guo, Yuanfang Yang, Yang Shen, Hen Tao |
| author_facet | Zhang, Jiaquan Qin, Caiyan Bian, Haoyu Cai, Libin Lu, Yi Zhang, Chaoning Dong, Wei Guo, Yuanfang Yang, Yang Shen, Hen Tao |
| contents | Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dynamics under varying parameter configurations through explicit conditioning on physical parameters. Theoretical analysis and extensive experiments on six PDEs demonstrate that AFNO improves long-horizon prediction stability and consistently reduces rollout errors compared with the baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25413 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Autoregression-Free Neural Operators for Time-Dependent PDEs Zhang, Jiaquan Qin, Caiyan Bian, Haoyu Cai, Libin Lu, Yi Zhang, Chaoning Dong, Wei Guo, Yuanfang Yang, Yang Shen, Hen Tao Machine Learning Artificial Intelligence Numerical Analysis Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dynamics under varying parameter configurations through explicit conditioning on physical parameters. Theoretical analysis and extensive experiments on six PDEs demonstrate that AFNO improves long-horizon prediction stability and consistently reduces rollout errors compared with the baselines. |
| title | Autoregression-Free Neural Operators for Time-Dependent PDEs |
| topic | Machine Learning Artificial Intelligence Numerical Analysis |
| url | https://arxiv.org/abs/2605.25413 |