PILD: Physics-Informed Learning via Diffusion
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_ | 1866918312935424000 |
|---|---|
| author | Zeng, Tianyi Wang, Tianyi Zhang, Jiaru Zeng, Zimo Zhang, Feiyang Xu, Yiming Chen, Sikai Zou, Yajie Wang, Yangyang Jiao, Junfeng Claudel, Christian Chen, Xinbo |
| author_facet | Zeng, Tianyi Wang, Tianyi Zhang, Jiaru Zeng, Zimo Zhang, Feiyang Xu, Yiming Chen, Sikai Zou, Yajie Wang, Yangyang Jiao, Junfeng Claudel, Christian Chen, Xinbo |
| contents | Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and first-principles physical constraints by introducing a virtual residual observation sampled from a Laplace distribution to supervise generation during training. To further integrate physical laws, a conditional embedding module is incorporated to inject physical information into the denoising network at multiple layers, ensuring consistent guidance throughout the diffusion process. The proposed PILD framework is concise, modular, and broadly applicable to problems governed by ordinary differential equations, partial differential equations, as well as algebraic equations or inequality constraints. Extensive experiments across engineering and scientific tasks including estimating vehicle trajectories, tire forces, Darcy flow and plasma dynamics, demonstrate that our PILD substantially improves accuracy, stability, and generalization over existing physics-informed and diffusion-based baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PILD: Physics-Informed Learning via Diffusion Zeng, Tianyi Wang, Tianyi Zhang, Jiaru Zeng, Zimo Zhang, Feiyang Xu, Yiming Chen, Sikai Zou, Yajie Wang, Yangyang Jiao, Junfeng Claudel, Christian Chen, Xinbo Machine Learning Artificial Intelligence Emerging Technologies Analysis of PDEs Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and first-principles physical constraints by introducing a virtual residual observation sampled from a Laplace distribution to supervise generation during training. To further integrate physical laws, a conditional embedding module is incorporated to inject physical information into the denoising network at multiple layers, ensuring consistent guidance throughout the diffusion process. The proposed PILD framework is concise, modular, and broadly applicable to problems governed by ordinary differential equations, partial differential equations, as well as algebraic equations or inequality constraints. Extensive experiments across engineering and scientific tasks including estimating vehicle trajectories, tire forces, Darcy flow and plasma dynamics, demonstrate that our PILD substantially improves accuracy, stability, and generalization over existing physics-informed and diffusion-based baselines. |
| title | PILD: Physics-Informed Learning via Diffusion |
| topic | Machine Learning Artificial Intelligence Emerging Technologies Analysis of PDEs |
| url | https://arxiv.org/abs/2601.21284 |