Spectral-inspired Operator Learning with Limited Data and Unknown Physics
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918517057519616 |
|---|---|
| author | Wan, Han Zhang, Rui Sun, Hao |
| author_facet | Wan, Han Zhang, Rui Sun, Hao |
| contents | Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability. To address these challenges, we propose Spectral-Inspired Neural Operator (SINO), which can model complex systems from just 2-5 trajectories, without requiring explicit PDE terms. Specifically, SINO automatically captures both local and global spatial derivatives from frequency indices, enabling a compact representation of the underlying differential operators in physics-agnostic regimes. To model nonlinear effects, it employs a Pi-block that performs multiplicative operations on spectral features, complemented by a low-pass filter to suppress aliasing. Extensive experiments on both 2D and 3D PDE benchmarks demonstrate that SINO achieves state-of-the-art performance, with improvements of 1-2 orders of magnitude in accuracy. Particularly, with only 5 training trajectories, SINO outperforms data-driven methods trained on 1000 trajectories and remains predictive on challenging out-of-distribution cases where other methods fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral-inspired Operator Learning with Limited Data and Unknown Physics Wan, Han Zhang, Rui Sun, Hao Machine Learning Artificial Intelligence Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability. To address these challenges, we propose Spectral-Inspired Neural Operator (SINO), which can model complex systems from just 2-5 trajectories, without requiring explicit PDE terms. Specifically, SINO automatically captures both local and global spatial derivatives from frequency indices, enabling a compact representation of the underlying differential operators in physics-agnostic regimes. To model nonlinear effects, it employs a Pi-block that performs multiplicative operations on spectral features, complemented by a low-pass filter to suppress aliasing. Extensive experiments on both 2D and 3D PDE benchmarks demonstrate that SINO achieves state-of-the-art performance, with improvements of 1-2 orders of magnitude in accuracy. Particularly, with only 5 training trajectories, SINO outperforms data-driven methods trained on 1000 trajectories and remains predictive on challenging out-of-distribution cases where other methods fail. |
| title | Spectral-inspired Operator Learning with Limited Data and Unknown Physics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2505.21573 |