A Neural PDE Solver with Temporal Stencil Modeling
Authors: Zhiqing Sun, Yiming Yang, Shinjae Yoo
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows |
| Researcher Affiliation | Academia | 1Carnegie Mellon University, Pittsburgh, PA 15213, USA 2Brookhaven National Laboratory, Upton, NY 11973, USA. |
| Pseudocode | No | No pseudocode or algorithm blocks are present in the paper. |
| Open Source Code | Yes | Our code is available at https: //github.com/Edward-Sun/TSM-PDE. |
| Open Datasets | No | Simulated data Following previous work (Kochkov et al., 2021), we train our method with 2-D Kolmogorov flow, a variant of incompressible Navier-Stokes flow with constant forcing f = sin(4y)ˆx 0.1u. All training and evaluation data are generated with a JAX-based2 finite volume-based direct numerical simulator in a staggered-square mesh (Mc Donough, 2007) as briefly described in Sec. 3.1. We refer the readers to the appendix of (Kochkov et al., 2021) for more data generation details. |
| Dataset Splits | No | We use 16 trajectories for evaluation. |
| Hardware Specification | Yes | We train and evaluate all the classic and neural Navier-Stokes solvers in 8 Nvidia Tesla V100-32G GPUs. The inference latency is measured by unrolling 2 trajectories for 25.0 simulation time on a single V100 GPU. |
| Software Dependencies | No | All training and evaluation data are generated with a JAX-based2 finite volume-based direct numerical simulator |
| Experiment Setup | Yes | We train the neural models on Re = 1000 flow data with density ρ = 1 and viscosity ν = 0.001 on a 2π x 2π domain, which results in a time-step of Δt = 7.0125 x 10−3 according to the Courant Friedrichs Lewy (CFD) condition on the 64x64 simulation grid. |