中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 计算技术研究所
  3. 中国科学院计算技术研究所
  4. 中国科学院计算技术研究所期刊论文
  5. 英文
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

文献类型：期刊论文

作者Zhang, Rui4; Meng, Qi1; Zhu, Rongchan2; Wang, Yue3; Shi, Wenlei5; Zhang, Shihua1; Ma, Zhi-Ming1; Liu, Tie-Yan6
刊名IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
出版日期2025-06-01
卷号47期号:6页码:5059-5075
关键词Training Monte Carlo methods Spatiotemporal phenomena Accuracy Probabilistic logic Neural networks Numerical models Mathematical models Finite difference methods Diffusion processes Neural PDE solver Monte Carlo method Feynman-Kac formula AI for PDE
ISSN号0162-8828
DOI10.1109/TPAMI.2025.3548673
英文摘要In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical algorithms, such as finite difference and pseudo-spectral methods, integrated during the training stage. These methods necessitate careful spatiotemporal discretization to achieve reasonable accuracy, leading to significant computational challenges and inaccurate simulations, particularly in cases with substantial spatiotemporal variations. To address these limitations, we propose the Monte Carlo Neural PDE Solver (MCNP Solver) for training unsupervised neural solvers via the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Compared to other unsupervised methods, MCNP Solver naturally inherits the advantages of the Monte Carlo method, which is robust against spatiotemporal variations and can tolerate coarse step size. In simulating the trajectories of particles, we employ Heun's method for the convection process and calculate the expectation via the probability density function of neighbouring grid points during the diffusion process. These techniques enhance accuracy and circumvent the computational issues associated with Monte Carlo sampling. Our numerical experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency compared to other unsupervised baselines.
资助项目NSFC[9247010235] ; National Key Research and Development Program of China[2019YFA0709501] ; CAS Project for Young Scientists in Basic Research[YSBR-034]
WOS研究方向Computer Science ; Engineering
语种英语
WOS记录号WOS:001484716600041
出版者IEEE COMPUTER SOC
源URL[http://119.78.100.204/handle/2XEOYT63/42379]  
专题中国科学院计算技术研究所期刊论文_英文
通讯作者Meng, Qi
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Beijing Inst Technol, Beijing 100081, Peoples R China
3.Beijing Jiaotong Univ, Beijing 100044, Peoples R China
4.Renmin Univ China, Gaoling Sch Artificial Intelligence, Beijing 100872, Peoples R China
5.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
6.Zhongguancun Acad, Beijing 100094, Peoples R China
推荐引用方式
GB/T 7714		 Zhang, Rui,Meng, Qi,Zhu, Rongchan,et al. Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2025,47(6):5059-5075.
APA Zhang, Rui.,Meng, Qi.,Zhu, Rongchan.,Wang, Yue.,Shi, Wenlei.,...&Liu, Tie-Yan.(2025).Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,47(6),5059-5075.
MLA Zhang, Rui,et al."Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation".IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 47.6(2025):5059-5075.

入库方式： OAI收割

来源：计算技术研究所

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。