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.