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erbacher/PDEBench-1D

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Hugging Face2023-12-20 更新2024-03-04 收录
下载链接：
https://hf-mirror.com/datasets/erbacher/PDEBench-1D
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资源简介：
--- dataset_info: - config_name: Advection_Sols_beta0.1 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1030317301 dataset_size: 2079020000 - config_name: Advection_Sols_beta0.2 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1034054442 dataset_size: 2079020000 - config_name: Advection_Sols_beta0.4 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1037220772 dataset_size: 2079020000 - config_name: Advection_Sols_beta0.7 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1039496575 dataset_size: 2079020000 - config_name: Advection_Sols_beta1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1041009183 dataset_size: 2079020000 - config_name: Advection_Sols_beta2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1041263590 dataset_size: 2079020000 - config_name: Advection_Sols_beta4.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1041302186 dataset_size: 2079020000 - config_name: Advection_Sols_beta7.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2079020000 num_examples: 10000 download_size: 1041314010 dataset_size: 2079020000 - config_name: Burgers_Sols_Nu0.001 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975050000.0 num_examples: 9500 - name: dev num_bytes: 51975000.0 num_examples: 250 - name: test num_bytes: 51975000.0 num_examples: 250 download_size: 1028326119 dataset_size: 2079000000.0 - config_name: Burgers_Sols_Nu0.002 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975050000.0 num_examples: 9500 - name: dev num_bytes: 51975000.0 num_examples: 250 - name: test num_bytes: 51975000.0 num_examples: 250 download_size: 1034543373 dataset_size: 2079000000.0 - config_name: Burgers_Sols_Nu0.004 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975050000.0 num_examples: 9500 - name: dev num_bytes: 51975000.0 num_examples: 250 - name: test num_bytes: 51975000.0 num_examples: 250 download_size: 1039636457 dataset_size: 2079000000.0 - config_name: Burgers_Sols_Nu0.01 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975040500.0 num_examples: 9500 - name: dev num_bytes: 51974750.0 num_examples: 250 - name: test num_bytes: 51974750.0 num_examples: 250 download_size: 1042820960 dataset_size: 2078990000.0 - config_name: Burgers_Sols_Nu0.02 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975040500.0 num_examples: 9500 - name: dev num_bytes: 51974750.0 num_examples: 250 - name: test num_bytes: 51974750.0 num_examples: 250 download_size: 1043138323 dataset_size: 2078990000.0 - config_name: Burgers_Sols_Nu0.04 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975040500.0 num_examples: 9500 - name: dev num_bytes: 51974750.0 num_examples: 250 - name: test num_bytes: 51974750.0 num_examples: 250 download_size: 1035623715 dataset_size: 2078990000.0 - config_name: Burgers_Sols_Nu0.1 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 995415792 dataset_size: 2078980000.0 - config_name: Burgers_Sols_Nu0.2 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 949166113 dataset_size: 2078980000.0 - config_name: Burgers_Sols_Nu0.4 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 847341109 dataset_size: 2078980000.0 - config_name: Burgers_Sols_Nu1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 573087335 dataset_size: 2078980000.0 - config_name: Burgers_Sols_Nu2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 315101631 dataset_size: 2078980000.0 - config_name: Burgers_Sols_Nu4.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1975031000.0 num_examples: 9500 - name: dev num_bytes: 51974500.0 num_examples: 250 - name: test num_bytes: 51974500.0 num_examples: 250 download_size: 189417705 dataset_size: 2078980000.0 - config_name: CFD_Rand_Eta0.01_Zeta0.01_periodic features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2099620000 num_examples: 10000 download_size: 1576405761 dataset_size: 2099620000 - config_name: CFD_Rand_Eta0.1_Zeta0.1_periodic features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2099600000 num_examples: 10000 download_size: 946984963 dataset_size: 2099600000 - config_name: CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2099640000 num_examples: 10000 download_size: 1573309616 dataset_size: 2099640000 - config_name: CFD_Rand_Eta1.e-8_Zeta1.e-8_trans features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 2099610000 num_examples: 10000 download_size: 0 dataset_size: 2099610000 - config_name: ReacDiff_Nu0.5_Rho1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 103983829 dataset_size: 1055010000 - config_name: ReacDiff_Nu0.5_Rho10.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055020000 num_examples: 10000 download_size: 124933565 dataset_size: 1055020000 - config_name: ReacDiff_Nu0.5_Rho2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 193004745 dataset_size: 1055010000 - config_name: ReacDiff_Nu0.5_Rho5.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 146090506 dataset_size: 1055010000 - config_name: ReacDiff_Nu1.0_Rho1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 217153008 dataset_size: 1055010000 - config_name: ReacDiff_Nu1.0_Rho10.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055020000 num_examples: 10000 download_size: 113039664 dataset_size: 1055020000 - config_name: ReacDiff_Nu1.0_Rho2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 139659779 dataset_size: 1055010000 - config_name: ReacDiff_Nu1.0_Rho5.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 121216648 dataset_size: 1055010000 - config_name: ReacDiff_Nu2.0_Rho1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 57854036 dataset_size: 1055010000 - config_name: ReacDiff_Nu2.0_Rho10.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055020000 num_examples: 10000 download_size: 73754842 dataset_size: 1055020000 - config_name: ReacDiff_Nu2.0_Rho2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 122071454 dataset_size: 1055010000 - config_name: ReacDiff_Nu2.0_Rho5.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 74329093 dataset_size: 1055010000 - config_name: ReacDiff_Nu5.0_Rho1.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 158789252 dataset_size: 1055010000 - config_name: ReacDiff_Nu5.0_Rho10.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055020000 num_examples: 10000 download_size: 55445429 dataset_size: 1055020000 - config_name: ReacDiff_Nu5.0_Rho2.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 58220881 dataset_size: 1055010000 - config_name: ReacDiff_Nu5.0_Rho5.0 features: - name: parameters dtype: string - name: tensor sequence: sequence: sequence: float32 splits: - name: train num_bytes: 1055010000 num_examples: 10000 download_size: 57392368 dataset_size: 1055010000 configs: - config_name: Advection_Sols_beta0.1 data_files: - split: train path: Advection_Sols_beta0.1/train-* - config_name: Advection_Sols_beta0.2 data_files: - split: train path: Advection_Sols_beta0.2/train-* - config_name: Advection_Sols_beta0.4 data_files: - split: train path: Advection_Sols_beta0.4/train-* - config_name: Advection_Sols_beta0.7 data_files: - split: train path: Advection_Sols_beta0.7/train-* - config_name: Advection_Sols_beta1.0 data_files: - split: train path: Advection_Sols_beta1.0/train-* - config_name: Advection_Sols_beta2.0 data_files: - split: train path: Advection_Sols_beta2.0/train-* - config_name: Advection_Sols_beta4.0 data_files: - split: train path: Advection_Sols_beta4.0/train-* - config_name: Advection_Sols_beta7.0 data_files: - split: train path: Advection_Sols_beta7.0/train-* - config_name: Burgers_Sols_Nu0.001 data_files: - split: train path: Burgers_Sols_Nu0.001/train-* - split: dev path: Burgers_Sols_Nu0.001/dev-* - split: test path: Burgers_Sols_Nu0.001/test-* - config_name: Burgers_Sols_Nu0.002 data_files: - split: train path: Burgers_Sols_Nu0.002/train-* - split: dev path: Burgers_Sols_Nu0.002/dev-* - split: test path: Burgers_Sols_Nu0.002/test-* - config_name: Burgers_Sols_Nu0.004 data_files: - split: train path: Burgers_Sols_Nu0.004/train-* - split: dev path: Burgers_Sols_Nu0.004/dev-* - split: test path: Burgers_Sols_Nu0.004/test-* - config_name: Burgers_Sols_Nu0.01 data_files: - split: train path: Burgers_Sols_Nu0.01/train-* - split: dev path: Burgers_Sols_Nu0.01/dev-* - split: test path: Burgers_Sols_Nu0.01/test-* - config_name: Burgers_Sols_Nu0.02 data_files: - split: train path: Burgers_Sols_Nu0.02/train-* - split: dev path: Burgers_Sols_Nu0.02/dev-* - split: test path: Burgers_Sols_Nu0.02/test-* - config_name: Burgers_Sols_Nu0.04 data_files: - split: train path: Burgers_Sols_Nu0.04/train-* - split: dev path: Burgers_Sols_Nu0.04/dev-* - split: test path: Burgers_Sols_Nu0.04/test-* - config_name: Burgers_Sols_Nu0.1 data_files: - split: train path: Burgers_Sols_Nu0.1/train-* - split: dev path: Burgers_Sols_Nu0.1/dev-* - split: test path: Burgers_Sols_Nu0.1/test-* - config_name: Burgers_Sols_Nu0.2 data_files: - split: train path: Burgers_Sols_Nu0.2/train-* - split: dev path: Burgers_Sols_Nu0.2/dev-* - split: test path: Burgers_Sols_Nu0.2/test-* - config_name: Burgers_Sols_Nu0.4 data_files: - split: train path: Burgers_Sols_Nu0.4/train-* - split: dev path: Burgers_Sols_Nu0.4/dev-* - split: test path: Burgers_Sols_Nu0.4/test-* - config_name: Burgers_Sols_Nu1.0 data_files: - split: train path: Burgers_Sols_Nu1.0/train-* - split: dev path: Burgers_Sols_Nu1.0/dev-* - split: test path: Burgers_Sols_Nu1.0/test-* - config_name: Burgers_Sols_Nu2.0 data_files: - split: train path: Burgers_Sols_Nu2.0/train-* - split: dev path: Burgers_Sols_Nu2.0/dev-* - split: test path: Burgers_Sols_Nu2.0/test-* - config_name: Burgers_Sols_Nu4.0 data_files: - split: train path: Burgers_Sols_Nu4.0/train-* - split: dev path: Burgers_Sols_Nu4.0/dev-* - split: test path: Burgers_Sols_Nu4.0/test-* - config_name: CFD_Rand_Eta0.01_Zeta0.01_periodic data_files: - split: train path: CFD_Rand_Eta0.01_Zeta0.01_periodic/train-* - config_name: CFD_Rand_Eta0.1_Zeta0.1_periodic data_files: - split: train path: CFD_Rand_Eta0.1_Zeta0.1_periodic/train-* - config_name: CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic data_files: - split: train path: CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic/train-* - config_name: CFD_Rand_Eta1.e-8_Zeta1.e-8_trans data_files: - split: train path: CFD_Rand_Eta1.e-8_Zeta1.e-8_trans/train-* - config_name: ReacDiff_Nu0.5_Rho1.0 data_files: - split: train path: ReacDiff_Nu0.5_Rho1.0/train-* - config_name: ReacDiff_Nu0.5_Rho10.0 data_files: - split: train path: ReacDiff_Nu0.5_Rho10.0/train-* - config_name: ReacDiff_Nu0.5_Rho2.0 data_files: - split: train path: ReacDiff_Nu0.5_Rho2.0/train-* - config_name: ReacDiff_Nu0.5_Rho5.0 data_files: - split: train path: ReacDiff_Nu0.5_Rho5.0/train-* - config_name: ReacDiff_Nu1.0_Rho1.0 data_files: - split: train path: ReacDiff_Nu1.0_Rho1.0/train-* - config_name: ReacDiff_Nu1.0_Rho10.0 data_files: - split: train path: ReacDiff_Nu1.0_Rho10.0/train-* - config_name: ReacDiff_Nu1.0_Rho2.0 data_files: - split: train path: ReacDiff_Nu1.0_Rho2.0/train-* - config_name: ReacDiff_Nu1.0_Rho5.0 data_files: - split: train path: ReacDiff_Nu1.0_Rho5.0/train-* - config_name: ReacDiff_Nu2.0_Rho1.0 data_files: - split: train path: ReacDiff_Nu2.0_Rho1.0/train-* - config_name: ReacDiff_Nu2.0_Rho10.0 data_files: - split: train path: ReacDiff_Nu2.0_Rho10.0/train-* - config_name: ReacDiff_Nu2.0_Rho2.0 data_files: - split: train path: ReacDiff_Nu2.0_Rho2.0/train-* - config_name: ReacDiff_Nu2.0_Rho5.0 data_files: - split: train path: ReacDiff_Nu2.0_Rho5.0/train-* - config_name: ReacDiff_Nu5.0_Rho1.0 data_files: - split: train path: ReacDiff_Nu5.0_Rho1.0/train-* - config_name: ReacDiff_Nu5.0_Rho10.0 data_files: - split: train path: ReacDiff_Nu5.0_Rho10.0/train-* - config_name: ReacDiff_Nu5.0_Rho2.0 data_files: - split: train path: ReacDiff_Nu5.0_Rho2.0/train-* - config_name: ReacDiff_Nu5.0_Rho5.0 data_files: - split: train path: ReacDiff_Nu5.0_Rho5.0/train-* --- # Dataset Card for "PDEBench-1D" [More Information needed](https://github.com/huggingface/datasets/blob/main/CONTRIBUTING.md#how-to-contribute-to-the-dataset-cards)

数据集信息： 1. 基础说明：本数据集为PDEBench-1D，包含四类偏微分方程（PDE）相关的数值解数据集，分别为平流方程解数据集、伯格斯方程解数据集、计算流体动力学（Computational Fluid Dynamics, CFD）随机数据集以及反应扩散（Reaction-Diffusion, ReacDiff）方程解数据集。 2. 各配置项详情： （1）平流方程解数据集（Advection_Sols系列，共8个配置）： 配置名称分别为Advection_Sols_beta0.1至Advection_Sols_beta7.0，β取值覆盖0.1、0.2、0.4、0.7、1.0、2.0、4.0、7.0。每个配置仅包含训练集划分，样本数为10000，字节数为2079020000，数据集总大小均为2079020000，下载大小略有差异。特征包含字符串类型的`parameters`参数特征，以及三层嵌套32位浮点型（float32）张量特征。 （2）伯格斯方程解数据集（Burgers_Sols系列，共12个配置）： 配置名称分别为Burgers_Sols_Nu0.001至Burgers_Sols_Nu4.0，ν取值覆盖0.001、0.002、0.004、0.01、0.02、0.04、0.1、0.2、0.4、1.0、2.0、4.0。每个配置包含训练集（9500样本）、验证集（dev，250样本）与测试集（test，250样本），总样本数为10000，数据集总大小约为2079000000，下载大小各异。特征与平流方程解数据集一致。 （3）CFD随机数据集（CFD_Rand系列，共4个配置）： 配置分别为CFD_Rand_Eta0.01_Zeta0.01_periodic、CFD_Rand_Eta0.1_Zeta0.1_periodic、CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic与CFD_Rand_Eta1.e-8_Zeta1.e-8_trans，其中前三者为周期性边界条件，最后一个为trans配置。每个配置仅包含训练集，样本数为10000，字节数约为2099600000，下载大小各异，其中CFD_Rand_Eta1.e-8_Zeta1.e-8_trans的下载大小为0。特征与前述配置一致。 （4）反应扩散方程解数据集（ReacDiff系列，共16个配置）： 配置名称覆盖Nu与Rho的不同组合，Nu取值为0.5、1.0、2.0、5.0，Rho取值为1.0、2.0、5.0、10.0，共4×4=16个配置。每个配置仅包含训练集，样本数为10000，字节数约为1055000000，下载大小各异。特征与前述配置一致。 3. 配置数据文件路径： 所有配置的训练/验证/测试数据均对应以配置名称为目录的`train-*`、`dev-*`、`test-*`文件路径，具体如下： - Advection_Sols系列配置仅包含训练集路径：`[配置名]/train-*` - Burgers_Sols系列配置包含训练集、验证集与测试集路径：`[配置名]/train-*`、`[配置名]/dev-*`、`[配置名]/test-*` - CFD_Rand系列配置仅包含训练集路径：`[配置名]/train-*` - ReacDiff系列配置仅包含训练集路径：`[配置名]/train-*` # “PDEBench-1D”数据集卡片 需补充更多信息，链接：https://github.com/huggingface/datasets/blob/main/CONTRIBUTING.md#how-to-contribute-to-the-dataset-cards
提供机构：
erbacher
原始信息汇总

数据集概述

数据集配置

Advection_Sols_beta系列

  • Advection_Sols_beta0.1

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,030,317,301字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta0.2

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,034,054,442字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta0.4

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,037,220,772字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta0.7

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,039,496,575字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta1.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,041,009,183字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta2.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,041,263,590字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta4.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,041,302,186字节
    • 数据集大小: 2,079,020,000字节

  • Advection_Sols_beta7.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,079,020,000字节, 10,000个样本
    • 下载大小: 1,041,314,010字节
    • 数据集大小: 2,079,020,000字节

Burgers_Sols_Nu系列

  • Burgers_Sols_Nu0.001

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,050,000字节, 9,500个样本
      • dev: 51,975,000字节, 250个样本
      • test: 51,975,000字节, 250个样本
    • 下载大小: 1,028,326,119字节
    • 数据集大小: 2,079,000,000字节

  • Burgers_Sols_Nu0.002

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,050,000字节, 9,500个样本
      • dev: 51,975,000字节, 250个样本
      • test: 51,975,000字节, 250个样本
    • 下载大小: 1,034,543,373字节
    • 数据集大小: 2,079,000,000字节

  • Burgers_Sols_Nu0.004

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,050,000字节, 9,500个样本
      • dev: 51,975,000字节, 250个样本
      • test: 51,975,000字节, 250个样本
    • 下载大小: 1,039,636,457字节
    • 数据集大小: 2,079,000,000字节

  • Burgers_Sols_Nu0.01

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,040,500字节, 9,500个样本
      • dev: 51,974,750字节, 250个样本
      • test: 51,974,750字节, 250个样本
    • 下载大小: 1,042,820,960字节
    • 数据集大小: 2,078,990,000字节

  • Burgers_Sols_Nu0.02

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,040,500字节, 9,500个样本
      • dev: 51,974,750字节, 250个样本
      • test: 51,974,750字节, 250个样本
    • 下载大小: 1,043,138,323字节
    • 数据集大小: 2,078,990,000字节

  • Burgers_Sols_Nu0.04

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,040,500字节, 9,500个样本
      • dev: 51,974,750字节, 250个样本
      • test: 51,974,750字节, 250个样本
    • 下载大小: 1,035,623,715字节
    • 数据集大小: 2,078,990,000字节

  • Burgers_Sols_Nu0.1

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 995,415,792字节
    • 数据集大小: 2,078,980,000字节

  • Burgers_Sols_Nu0.2

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 949,166,113字节
    • 数据集大小: 2,078,980,000字节

  • Burgers_Sols_Nu0.4

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 847,341,109字节
    • 数据集大小: 2,078,980,000字节

  • Burgers_Sols_Nu1.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 573,087,335字节
    • 数据集大小: 2,078,980,000字节

  • Burgers_Sols_Nu2.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 315,101,631字节
    • 数据集大小: 2,078,980,000字节

  • Burgers_Sols_Nu4.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,975,031,000字节, 9,500个样本
      • dev: 51,974,500字节, 250个样本
      • test: 51,974,500字节, 250个样本
    • 下载大小: 189,417,705字节
    • 数据集大小: 2,078,980,000字节

CFD_Rand_Eta_Zeta系列

  • CFD_Rand_Eta0.01_Zeta0.01_periodic

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,099,620,000字节, 10,000个样本
    • 下载大小: 1,576,405,761字节
    • 数据集大小: 2,099,620,000字节

  • CFD_Rand_Eta0.1_Zeta0.1_periodic

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,099,600,000字节, 10,000个样本
    • 下载大小: 946,984,963字节
    • 数据集大小: 2,099,600,000字节

  • CFD_Rand_Eta1.e-8_Zeta1.e-8_periodic

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,099,640,000字节, 10,000个样本
    • 下载大小: 1,573,309,616字节
    • 数据集大小: 2,099,640,000字节

  • CFD_Rand_Eta1.e-8_Zeta1.e-8_trans

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 2,099,610,000字节, 10,000个样本
    • 下载大小: 0字节
    • 数据集大小: 2,099,610,000字节

ReacDiff_Nu_Rho系列

  • ReacDiff_Nu0.5_Rho1.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,055,010,000字节, 10,000个样本
    • 下载大小: 103,983,829字节
    • 数据集大小: 1,055,010,000字节

  • ReacDiff_Nu0.5_Rho10.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,055,020,000字节, 10,000个样本
    • 下载大小: 124,933,565字节
    • 数据集大小: 1,055,020,000字节

  • ReacDiff_Nu0.5_Rho2.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,055,010,000字节, 10,000个样本
    • 下载大小: 193,004,745字节
    • 数据集大小: 1,055,010,000字节

  • ReacDiff_Nu0.5_Rho5.0

    • 特征:
      • parameters: string
      • tensor: float32序列的序列的序列
    • 分割:
      • train: 1,055,010,0
搜集汇总
数据集介绍
main_image_url
构建方式
PDEBench-1D数据集的构建基于一系列偏微分方程（PDE）的数值解，涵盖了多种物理和工程领域中的典型问题。数据集通过模拟不同参数配置下的PDE解，生成了一系列高维张量数据。每个配置对应一个特定的PDE类型及其参数设置，确保了数据集的多样性和广泛适用性。
特点
PDEBench-1D数据集的特点在于其高维张量数据的复杂性和多样性。数据集包含了多种PDE类型及其参数配置，涵盖了从简单到复杂的不同场景。此外，数据集的结构设计使得每个样本都包含详细的参数信息和相应的张量数据，便于研究人员进行深入分析和模型训练。
使用方法
使用PDEBench-1D数据集时，研究人员可以利用其高维张量数据进行模型训练和验证，以解决各种偏微分方程相关的问题。数据集的结构设计使得用户可以轻松访问和处理不同配置下的PDE解数据。通过加载数据集中的特定配置，用户可以提取所需的参数和数据，进行进一步的分析和建模。
背景与挑战
背景概述
PDEBench-1D数据集由Erbacher等人创建，专注于一维偏微分方程（PDE）的数值解法。该数据集的核心研究问题是如何在高维空间中有效模拟和预测PDE的行为，这对于流体力学、热传导和量子力学等领域的研究具有重要意义。主要研究人员和机构通过模拟多种PDE配置，生成了大量数据，旨在为机器学习和深度学习算法提供丰富的训练和测试资源。该数据集的创建不仅推动了PDE数值解法的发展，也为相关领域的研究提供了新的工具和方法。
当前挑战
PDEBench-1D数据集在构建过程中面临多项挑战。首先，生成高质量的PDE模拟数据需要高精度的数值方法和计算资源，这增加了数据集构建的复杂性和成本。其次，不同PDE配置的参数空间广泛，如何有效覆盖和验证这些参数组合是一个技术难题。此外，数据集的规模庞大，存储和处理这些数据对计算基础设施提出了高要求。最后，如何确保数据集的多样性和代表性，以便训练出的模型能够泛化到各种实际应用场景，也是该数据集面临的重要挑战。
常用场景
经典使用场景
在偏微分方程（PDE）的研究领域中，PDEBench-1D数据集被广泛用于训练和验证数值求解方法。该数据集包含了多种一维PDE的解，如Advection、Burgers和ReacDiff等方程，通过不同参数配置生成的大量数据样本。研究者利用这些数据进行模型训练，以提高数值求解的精度和效率，特别是在复杂边界条件和非线性问题中的应用。
衍生相关工作
基于PDEBench-1D数据集，研究者们开发了多种数值求解算法和优化模型。例如，一些工作提出了基于深度学习的PDE求解器，通过神经网络直接预测方程的解，显著提高了计算效率。此外，该数据集还促进了多尺度模拟方法的发展，使得在不同时间和空间尺度上的复杂系统模拟成为可能。这些衍生工作不仅丰富了PDE求解的理论基础，也为实际应用提供了新的解决方案。
数据集最近研究
最新研究方向
在偏微分方程（PDE）领域，PDEBench-1D数据集的最新研究方向主要集中在利用深度学习技术来高效求解和预测一维PDE的解。随着计算能力的提升和数据驱动方法的兴起，研究者们正探索如何通过神经网络模型来逼近复杂PDE的解，从而在科学计算和工程应用中实现更高的精度和效率。这一研究方向不仅有助于推动数值分析的前沿发展，还为解决实际工程问题提供了新的工具和方法。
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