PDEBench Datasets (doi:10.18419/darus-2986)

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Part 1: Document Description
Part 2: Study Description
Part 5: Other Study-Related Materials
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Document Description

Citation

Title:

PDEBench Datasets

Identification Number:

doi:10.18419/darus-2986

Distributor:

DaRUS

Date of Distribution:

2022-07-26

Version:

8

Bibliographic Citation:

Takamoto, Makoto; Praditia, Timothy; Leiteritz, Raphael; MacKinlay, Dan; Alesiani, Francesco; Pflüger, Dirk; Niepert, Mathias, 2022, "PDEBench Datasets", https://doi.org/10.18419/darus-2986, DaRUS, V8

Study Description

Citation

Title:

PDEBench Datasets

Subtitle:

Data for "PDEBench: An Extensive Benchmark for Scientific Machine Learning"

Identification Number:

doi:10.18419/darus-2986

Authoring Entity:

Takamoto, Makoto (NEC Labs Europe)

Praditia, Timothy (Universität Stuttgart)

Leiteritz, Raphael (Universität Stuttgart)

MacKinlay, Dan (CSIRO's Data61)

Alesiani, Francesco (NEC Labs Europe)

Pflüger, Dirk (Universität Stuttgart)

Niepert, Mathias (Universität Stuttgart)

Other identifications and acknowledgements:

Takamoto, Makoto

Other identifications and acknowledgements:

Praditia, Timothy

Other identifications and acknowledgements:

Leiteritz, Raphael

Other identifications and acknowledgements:

MacKinlay, Dan

Other identifications and acknowledgements:

Alesiani, Francesco

Other identifications and acknowledgements:

Pflüger, Dirk

Other identifications and acknowledgements:

Niepert, Mathias

Grant Number:

EXC 2075 - 390740016

Distributor:

DaRUS

Access Authority:

Leiteritz, Raphael

Access Authority:

Takamoto, Makoto

Access Authority:

Takamoto, Makoto

Access Authority:

MacKinlay, Dan

Access Authority:

Praditia, Timothy

Access Authority:

Alesiani, Francesco

Depositor:

Leiteritz, Raphael

Date of Deposit:

2022-06-08

Holdings Information:

https://doi.org/10.18419/darus-2986

Study Scope

Keywords:

Computer and Information Science, Earth and Environmental Sciences, Physics, Benchmark, Scientific Machine Learning, Machine Learning, Physics-Informed Machine Learning, Partial Differential Equation

Abstract:

<p>This dataset contains benchmark data, generated with numerical simulation based on different PDEs, namely 1D advection, 1D Burgers', 1D and 2D diffusion-reaction, 1D diffusion-sorption, 1D, 2D, and 3D compressible Navier-Stokes, 2D Darcy flow, and 2D shallow water equation. This dataset is intended to progress the scientific ML research area. In general, the data are stored in HDF5 format, with the array dimensions packed according to the convention [b,t,x1,...,xd,v], where b is the batch size (i.e. number of samples), t is the time dimension, x1,...,xd are the spatial dimensions, and v is the number of channels (i.e. number of variables of interest).</p> <p>More detailed information are also provided in our Github repository (<a href="https://github.com/pdebench/PDEBench">https://github.com/pdebench/PDEBench</a>) and our submitting paper to NeurIPS 2022 Benchmark track.</p>

Kind of Data:

HDF5 files

Notes:

This version includes the debugged version of advection and Burgers equation solutions.

Methodology and Processing

Sources Statement

Data Access

Other Study Description Materials

Related Materials

Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M.: <a href="https://github.com/pdebench/PDEBench">PDEBench</a>. Github repository. 2022

Related Studies

Makoto, T., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M. (2022): PDEBench Pretrained Models, <a href="https://doi.org/10.18419/darus-2987">doi: 10.18419/darus-2987</a>, DaRUS.

Related Publications

Citation

Title:

Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M.: PDEBench: An Extensive Benchmark for Scientific Machine Learning. submitted to the 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks.

Identification Number:

2210.07182

Bibliographic Citation:

Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M.: PDEBench: An Extensive Benchmark for Scientific Machine Learning. submitted to the 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks.

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1D_Advection_Sols_beta0.1.hdf5

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1D_Advection_Sols_beta0.2.hdf5

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1D_Advection_Sols_beta7.0.hdf5

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1D_Burgers_Sols_Nu0.001.hdf5

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1D_Burgers_Sols_Nu0.4.hdf5

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1D_Burgers_Sols_Nu4.0.hdf5

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1D_CFD_Rand_Eta0.01_Zeta0.01_periodic_Train.hdf5

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1D CFD Train data for random initial condition

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1D_CFD_Rand_Eta0.1_Zeta0.1_periodic_Train.hdf5

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1D CFD Train data for random initial condition

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1D_CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic_Train.hdf5

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1D CFD Train data for random initial condition

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1D_CFD_Rand_Eta1.e-8_Zeta1.e-8_trans_Train.hdf5

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CFD dataset (1D)

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1D_CFD_Shock_Eta1.e-8_Zeta1.e-8_trans_Train.hdf5

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CFD dataset (1D)

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Sod6.hdf5

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CFD dataset (1D)

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1D_diff-sorp_NA_NA.h5

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ReacDiff_Nu0.5_Rho1.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu0.5_Rho10.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu0.5_Rho2.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu0.5_Rho5.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu1.0_Rho1.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu1.0_Rho10.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu1.0_Rho2.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu1.0_Rho5.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu2.0_Rho1.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu2.0_Rho10.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu2.0_Rho2.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu2.0_Rho5.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu5.0_Rho1.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu5.0_Rho10.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu5.0_Rho2.0.hdf5

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ReactionDiffusion dataset (1D)

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ReacDiff_Nu5.0_Rho5.0.hdf5

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ReactionDiffusion dataset (1D)

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2D_CFD_Rand_M0.1_Eta0.01_Zeta0.01_periodic_128_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Rand_M0.1_Eta0.1_Zeta0.1_periodic_128_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Rand_M0.1_Eta1e-08_Zeta1e-08_periodic_512_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Rand_M1.0_Eta0.01_Zeta0.01_periodic_128_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Rand_M1.0_Eta0.1_Zeta0.1_periodic_128_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Rand_M1.0_Eta1e-08_Zeta1e-08_periodic_512_Train.hdf5

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2D CFD Train data for random initial condition

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2D_CFD_Turb_M0.1_Eta1e-08_Zeta1e-08_periodic_512_Train.hdf5

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2D CFD Train data for Turbulence initial condition

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2D_CFD_Turb_M1.0_Eta1e-08_Zeta1e-08_periodic_512_Train.hdf5

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2D CFD Train data for Turbulence initial condition

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2D_DarcyFlow_beta0.01_Train.hdf5

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DarcyFlow dataset (2D)

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2D_DarcyFlow_beta0.1_Train.hdf5

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DarcyFlow dataset (2D)

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2D_DarcyFlow_beta1.0_Train.hdf5

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DarcyFlow dataset (2D)

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2D_DarcyFlow_beta10.0_Train.hdf5

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DarcyFlow dataset (2D)

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2D_DarcyFlow_beta100.0_Train.hdf5

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DarcyFlow dataset (2D)

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2D_diff-react_NA_NA.h5

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ns_incom_inhom_2d_512-85.h5

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ns_incom_inhom_2d_512-86.h5

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ns_incom_inhom_2d_512-87.h5

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ns_incom_inhom_2d_512-88.h5

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ns_incom_inhom_2d_512-89.h5

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ns_incom_inhom_2d_512-90.h5

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ns_incom_inhom_2d_512-91.h5

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ns_incom_inhom_2d_512-92.h5

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ns_incom_inhom_2d_512-93.h5

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ns_incom_inhom_2d_512-94.h5

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ns_incom_inhom_2d_512-95.h5

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ns_incom_inhom_2d_512-96.h5

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3D_CFD_Rand_M0.1_Eta1e-08_Zeta1e-08_periodic_Train.hdf5

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3D_CFD_Rand_M1.0_Eta1e-08_Zeta1e-08_periodic_Train.hdf5

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