Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

1 code implementation • 10 Feb 2023 • Rui Zhang, Qi Meng, Rongchan Zhu, Yue Wang, Wenlei Shi, Shihua Zhang, Zhi-Ming Ma, Tie-Yan Liu

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.

Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equations

no code implementations • 20 Jun 2022 • Rui Zhang, Peiyan Hu, Qi Meng, Yue Wang, Rongchan Zhu, Bingguang Chen, Zhi-Ming Ma, Tie-Yan Liu

To this end, we propose the \emph{Deep Random Vortex Method} (DRVM), which combines the neural network with a random vortex dynamics system equivalent to the Navier-Stokes equation.

Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs

1 code implementation • 13 Apr 2022 • Peiyan Hu, Qi Meng, Bingguang Chen, Shiqi Gong, Yue Wang, Wei Chen, Rongchan Zhu, Zhi-Ming Ma, Tie-Yan Liu

Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics.

Large $N$ limit of the $O(N)$ linear sigma model in 3D

no code implementations • 4 Feb 2021 • Hao Shen, Rongchan Zhu, Xiangchan Zhu

We prove tightness of the invariant measures in the large N limit.

Quantization Probability Mathematical Physics Analysis of PDEs Mathematical Physics