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