PDEBench Pretrained Models

Version 1.0

Takamoto, Makoto; Praditia, Timothy; Leiteritz, Raphael; MacKinlay, Dan; Alesiani, Francesco; Pflüger, Dirk; Niepert, Mathias, 2022, "PDEBench Pretrained Models", https://doi.org/10.18419/darus-2987, DaRUS, V1

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Description	This dataset contains the pretrained baseline models, namely FNO, U-Net, and PINN. These models are trained on different PDEs, such as 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. In addition the dataset contains the pre-trained model for the 1D Inverse problem for FNO and U-Net. These models are stored using the same structure as the dataset they trained on. All the files are saved in .pt files, the default file type for the PyTorch library. 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, Physics-Informed Machine Learning, 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.
License/Data Use Agreement	CC BY 4.0

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	1DCFD_FNO.tar fno/TAR Archive - 2.6 MB Published Jun 21, 2022 29 Downloads MD5: f0ad9bb3bc212fd905038a2cfcb5b190 1D compressible NS eq pretrained model for FNO Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1DCFD_PINN.tar pinn/TAR Archive - 1.6 MB Published Jun 21, 2022 21 Downloads MD5: 06e1cb179ae9f4c45db41c31ef299288 1D compressible NS eq pretrained model for PINN Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1DCFD_Unet.tar unet/TAR Archive - 155.6 MB Published Jun 21, 2022 15 Downloads MD5: fe8713baef7d3a3bd4040b6c6c27d05e 1D compressible NS eq pretrained model for Unet Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1DReacDiff_FNO.tar fno/TAR Archive - 2.0 MB Published Jun 21, 2022 23 Downloads MD5: 5f40110c251c5f16aa94ca324bdc5630 1D Reaction-Diffusion eq pretrained model for FNO Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1DReacDiff_PINN.tar pinn/TAR Archive - 1.3 MB Published Jun 21, 2022 19 Downloads MD5: ed0913028a37b250547c732f726d2436 1D Reaction-Diffusion eq pretrained model for PINN Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1DReacDiff_Unet.tar unet/TAR Archive - 124.4 MB Published Jun 21, 2022 14 Downloads MD5: 7b0f0c181c03da2e1d7f2ccc0001663c 1D Reaction-Diffusion eq pretrained model for Unet Data	Access File File Access Public Download Options TAR Archive Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta4.0_FNO.pt 1D/Advection/Train/Unknown - 518.6 KB Published Jun 21, 2022 24 Downloads MD5: 38479648059adc6d77bf7c60911ddc35 Advection pre-trained model (FNO) (1D) Data	Access File File Access Public Download Options Original File Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Advection_Sols_beta4.0_Unet.pt 1D/Advection/Train/Unknown - 31.1 MB Published Jun 21, 2022 16 Downloads MD5: e37c31313eefd5568c11af0c36075834 Advection pre-trained model (Unet) (1D) Data	Access File File Access Public Download Options Original File Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Burgers_Sols_Nu1.0_FNO.pt 1D/Burgers/Train/Unknown - 518.6 KB Published Jun 21, 2022 37 Downloads MD5: 09510743c315a505c42e2da4c5313a9d Burgers pre-trained model (FNO) (1D) Data	Access File File Access Public Download Options Original File Format Download Metadata Data File Citation EndNote XML RIS BibTeX
	1D_Burgers_Sols_Nu1.0_Unet.pt 1D/Burgers/Train/Unknown - 31.1 MB Published Jun 21, 2022 19 Downloads MD5: fedc814f213e17be7338e493c6cffabe Burgers pre-trained model (Unet) (1D) Data	Access File File Access Public Download Options Original File Format Download Metadata Data File Citation EndNote XML RIS BibTeX

Citation Metadata

Persistent Identifier	doi:10.18419/darus-2987
Publication Date	2022-06-21
Title	PDEBench Pretrained Models
Subtitle	Pretrained models 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 the pretrained baseline models, namely FNO, U-Net, and PINN. These models are trained on different PDEs, such as 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. In addition the dataset contains the pre-trained model for the 1D Inverse problem for FNO and U-Net. These models are stored using the same structure as the dataset they trained on. All the files are saved in .pt files, the default file type for the PyTorch library. 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 (Wikidata) https://www.wikidata.org/wiki/Q816747 Scientific Machine Learning Physics-Informed Machine Learning Machine Learning (Wikidata) https://www.wikidata.org/wiki/Q2539 Partial Differential Equation (Wikidata) https://www.wikidata.org/wiki/Q271977
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.
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	2022-06-09
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 Datasets, doi: 10.18419/darus-2986, DaRUS.

Process Metadata

Processing Methods	Fourier Neural Operator (FNO) (FNO is a deep learning method that learns neural operator in the Fourier space.) ; Parameters: number of channels, modes, width U-Net (U-Net is a convolutional neural network architecture that learns the image-to-image mapping functions.) ; Parameters: number of channels, number of latent features Physics-Informed Neural Networks (PINN) (PINN is a deep neural network architecture that learns PDE surrogate representation using the automatic differentiation tools.) ; Parameters: number of hidden layers, number of nodes ADAM Optimizer (ADAM is a momentum-based stochastic gradient descent optimization method.) ; Parameters: learning rate, number of epochs, scheduler step, scheduler multiplier, weight decay
Method Parameters	weight (w) [-] bias (b) [-] learning rate (\alpha) [-] : 0.001 number of epochs (epochs) [-] : 500 scheduler step (patience) [-] : 100 scheduler multiplier (\gamma) [-] : 0.5 weight decay (\lambda) [-] : 0.0001
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) h5py Version: 3.6.0 (https://www.h5py.org/) BSD 3-Clause (Collette, A. Python and HDF5 (2013).) DeepXDE Version: 1.1.3 (https://github.com/lululxvi/deepxde) GNU Lesser General Public License v2.1 doi: (Lu, L., Meng, X., Mao, Z., Karniadakis, G.E. DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1), 208-228 (2021). doi: 10.1137/19M1274067) PyTorch Version: 1.11.0 (https://pytorch.org/) BSD 3-Clause (Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S. PyTorch: An Imperative Style, High-Performance Deep Learning Library. Advances in Neural Information Processing Systems 32, 8024-8035 (2019).)

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