Learned Simulators for Turbulence
Authors: Kim Stachenfeld, Drummond Buschman Fielding, Dmitrii Kochkov, Miles Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter Battaglia, Alvaro Sanchez-Gonzalez
ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We show that our proposed model can simulate turbulent dynamics more accurately than classical numerical solvers at the comparably low resolutions across various scientifically relevant metrics. Our model is trained end-to-end from data |
| Researcher Affiliation | Collaboration | 1Deep Mind, London, UK 2Center for Computational Astrophysics, Flatiron Institute, New York, NY 3Google Research, Cambridge, MA 4Princeton University, Princeton, NJ |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement about the release of its source code or a link to a code repository for the described methodology. |
| Open Datasets | Yes | The training data is generated at high resolution Spatial and temporal downsampling factors and additional details about the environments are shown in the Appendix. ... 1D Kuramoto-Sivashinsky Equation (KS-1D): ... solved using Fourier spectral method (Kuramoto, 1978; Sivashinsky, 1977). ... 2D Incompressible Decaying Turbulence (INCOMP-2D): ... solved using direct numerical simulation (Kochkov et al., 2021). ... 3D Compressible Decaying Turbulence (COMPDECAY-3D): ... Simulations were carried out with Athena++ (Stone et al., 2020). |
| Dataset Splits | Yes | Table B.1: # Trajectories Training 1000 190 27 20 if Lx = 0.75; Validation 100 10 4 1 per Lx; Test 100 10 4 1 per Lx |
| Hardware Specification | Yes | Training took up to a week on an NVIDIA V100 GPU. ... In comparison, the learned model’s runtime is 1s on an NVIDIA V100 GPU, and 20-30s on a 8-core CPU. |
| Software Dependencies | No | The paper mentions 'Tensor Flow' but does not provide specific version numbers for any software dependencies. |
| Experiment Setup | Yes | Loss All models are trained to predict X. We use a mean square error loss ℓ(Xt, Xt+Δt) = MSE(NN(Xt; θ), X) to optimize parameters θ. Input Xt and target X = Xt+Δt - Xt features are normalized to be zero-mean and unit variance... Optionally, we trained with Gaussian random noise with fixed standard deviation σ added to the input Xt... We trained the models for up to 10M steps, with exponential learning rate decay annealed from 1e-4 to 1e-7 in the first 6M steps. Models usually reached convergence at around 5M steps. ... Batch size 32 8 1 1 (4 if multisize) ... Noise 1e-2 1e-4 1e-2 1e-3 ... Constraint weight 1 1 |