PDEBench Datasets

Version 8.0

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

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Subtitle	Data for "PDEBench: An Extensive Benchmark for Scientific Machine Learning"
Description	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). More detailed information are also provided in our Github repository (https://github.com/pdebench/PDEBench) and our submitting paper to NeurIPS 2022 Benchmark track.
Subject	Computer and Information Science; Earth and Environmental Sciences; Physics
Keyword	Benchmark, Scientific Machine Learning, Machine Learning, Physics-Informed Machine Learning, Partial Differential Equation
Related Publication	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.arXiv: 2210.07182
Notes	This version includes the debugged version of advection and Burgers equation solutions.
Data Generation	Simulation
License/Data Use Agreement	CC BY 4.0

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	1D_Advection_Sols_beta0.1.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 561 Downloads MD5: b4be2fc3383f737c76033073e6d2ccfb DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta0.2.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 315 Downloads MD5: d47b52c1be4b6bcaa8748a8df2f5fbb8 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta0.4.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 281 Downloads MD5: d595bbfd2c659df995a93cd40d6ea568 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta0.7.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 207 Downloads MD5: f89030c240a1e90b55649776854a84c2 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta1.0.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 272 Downloads MD5: 1fe41923a4123db55bf4e89bea32e142 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta2.0.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 247 Downloads MD5: 0e9beff98693089c38e213a1f2b9ac43 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta4.0.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 267 Downloads MD5: a87b03ff425496360e2732921805f47d DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta7.0.hdf5 1D/Advection/Train/Hierarchical Data Format - 7.7 GB Published Oct 9, 2023 216 Downloads MD5: 72a286ad2fcba574bd20bc045ba82d58 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Burgers_Sols_Nu0.001.hdf5 1D/Burgers/Train/Hierarchical Data Format - 7.7 GB Published Nov 30, 2023 362 Downloads MD5: 44cb784d5a07aa2b1c864cabdcf625f9 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Burgers_Sols_Nu0.002.hdf5 1D/Burgers/Train/Hierarchical Data Format - 7.7 GB Published Nov 30, 2023 194 Downloads MD5: edf1cd13622d151dfde3e4e5af7a95b4 DATA	Access File File Access Public Download Options Hierarchical Data Format Download Metadata Data File Citation EndNote XML RIS BibTeX

Citation Metadata

Persistent Identifier	doi:10.18419/darus-2986
Publication Date	2022-07-26
Title	PDEBench Datasets
Subtitle	Data for "PDEBench: An Extensive Benchmark for Scientific Machine Learning"
Author	Takamoto, Makoto (NEC Labs Europe) - ORCID: 0000-0001-7192-1956 Praditia, Timothy (Universität Stuttgart) - ORCID: 0000-0003-3619-9122 Leiteritz, Raphael (Universität Stuttgart) - ORCID: 0000-0001-8070-2384 MacKinlay, Dan (CSIRO's Data61) - ORCID: 0000-0001-6077-2684 Alesiani, Francesco (NEC Labs Europe) - ORCID: 0000-0003-4413-7247 Pflüger, Dirk (Universität Stuttgart) - ORCID: 0000-0002-4360-0212 Niepert, Mathias (Universität Stuttgart) - ORCID: 0000-0002-8401-3751
Point of Contact	Use email button above to contact. Leiteritz, Raphael (Universität Stuttgart) Takamoto, Makoto (NEC Labs Europe) Takamoto, Makoto (NEC Labs Europe) MacKinlay, Dan (CSIRO's Data61) Praditia, Timothy (Universität Stuttgart) Alesiani, Francesco (NEC Labs Europe)
Description	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). More detailed information are also provided in our Github repository (https://github.com/pdebench/PDEBench) and our submitting paper to NeurIPS 2022 Benchmark track.
Subject	Computer and Information Science; Earth and Environmental Sciences; Physics
Keyword	Benchmark https://www.wikidata.org/wiki/Q816747 (Wikidata) Scientific Machine Learning Machine Learning https://www.wikidata.org/wiki/Q2539 (Wikidata) Physics-Informed Machine Learning Partial Differential Equation https://www.wikidata.org/wiki/Q271977 (Wikidata)
Related Publication	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. arXiv 2210.07182 https://arxiv.org/abs/2210.07182
Notes	This version includes the debugged version of advection and Burgers equation solutions.
Contributor	Project Leader : Takamoto, Makoto Researcher : Praditia, Timothy Researcher : Leiteritz, Raphael Researcher : MacKinlay, Dan Researcher : Alesiani, Francesco Supervisor : Pflüger, Dirk Supervisor : Niepert, Mathias
Funding Information	DFG: EXC 2075 - 390740016
Project	PDEBench
Depositor	Leiteritz, Raphael
Deposit Date	2022-06-08
Data Type	HDF5 files
Related Material	Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M.: PDEBench. Github repository. 2022
Related Dataset	Makoto, T., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M. (2022): PDEBench Pretrained Models, doi: 10.18419/darus-2987, DaRUS.

Process Metadata

Processing Methods

Finite Volume (Spatial discretization method used to integrate the spatial derivative terms in the PDEs.)
Runge-Kutta (Fourth order Runge-Kutta method is used to integrate the temporal derivative in the PDEs.) ; Parameters: error tolerance

Software

NumPy Version: 1.22.3 (https://numpy.org/) BSD 3-Clause (Harris, C.R., Millman, K.J., van der Walt, S.J. et al. Array programming with NumPy. Nature 585, 357-362 (2020). doi: 10.1038/s41586-020-2649-2)
SciPy Version: 1.8.0 (https://scipy.org/) BSD 3-Clause (Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, CJ Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E.A. Quintero, Charles R Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17(3), 261-272 (2020). doi: 10.1038/s41592-019-0686-2)
h5py Version: 3.6.0 (https://www.h5py.org/) BSD 3-Clause (Collette, A. Python and HDF5 (2013).)
Clawpack Version: 5.6.1 (https://www.clawpack.org/) BSD 3-Clause (Mandli, K.T., Ahmadia, A.J., Berger, M.J., Calhoun, D.A., George, D.L., Hadjimichael, Y., Ketcheson, D.I., Lemoine, G.I., LeVeque, R.J. Clawpack: building an open source ecosystem for solving hyperbolic PDEs. PeerJ Computer Science (2016). doi: 10.7717/peerj-cs.68)
JAX Version: 0.3.13 (https://jax.readthedocs.io/en/latest/index.html) Apache License 2.0 (Bradbury, J., Frostig, R., Hawkins, P., Johnson, M.J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., Zhang, Q. JAX: composable transformations of Python+NumPy programs (2018).)
PhiFlow Version: 2.0.3 (https://github.com/tum-pbs/PhiFlow) MIT (Thuerey, N., Um, K., Holl, P. ΦFlow: A Differentiable PDE Solving Framework for Deep Learning via Physical Simulations. Differential Computer Vision, Graphics, and Physics in Machine Learning workshop at NeurIPS 2020.)
pyDaRUS Version: 1.0.5 (https://github.com/JR-1991/pyDaRUS) MIT (Range, J. PyDaRUS. Github repository (2022).)

Engineering Metadata

Data Generation

Simulation

Measured Variables

Contaminant concentration (diffusion-sorption equation) (u) [kg/m^3]
Activator concentration (2D diffusion-reaction equation) (u) [-]
Inhibitor concentration (2D diffusion-reaction equation) (v) [-]
Water depth (shallow water equation) (h) [m]
mass density (compressible fluid dynamics) (rho) [kg/m^3]
velocity (compressible fluid dynamics) (v) [m/s]
pressure (compressible fluid dynamics) (p) [kg /m/s^2]

Dataset Terms

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Our Community Norms as well as good scientific practices expect that proper credit is given via citation. Please use the data citation shown on the dataset page.

Creative Commons Attribution 4.0 International License. CC BY 4.0

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