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[Doc] Add pretrained model for laplace2d & refine comments #639

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44261c8
update laplace2d pretrained model
HydrogenSulfate Nov 14, 2023
e21d730
Merge branch 'develop' into add_pretrain3
HydrogenSulfate Nov 15, 2023
9728b4a
remove 'after finished training' comment in evaluate function
HydrogenSulfate Nov 15, 2023
b3695f6
update README.md
HydrogenSulfate Nov 15, 2023
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46 changes: 23 additions & 23 deletions README.md
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Expand Up @@ -25,45 +25,45 @@ PaddleScience 是一个基于深度学习框架 PaddlePaddle 开发的科学计

| 问题类型 | 案例名称 | 优化算法 | 模型类型 | 训练方式 | 数据集 | 参考资料 |
|-----|---------|-----|---------|----|---------|---------|
| 微分方程 | [拉普拉斯方程](./docs/zh/examples/laplace2d.md) | 机理驱动 | MLP | 无监督学习 | - | - |
| 微分方程 | [伯格斯方程](./docs/zh/examples/deephpms.md) | 机理驱动 | MLP | 无监督学习 | [Data](https://github.com/maziarraissi/DeepHPMs/tree/master/Data) | [Paper](https://arxiv.org/pdf/1801.06637.pdf) |</center>
| 微分方程 | [非线性偏微分方程](./docs/zh/examples/pirbn.md) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://arxiv.org/abs/2304.06234) |
| 微分方程 | [洛伦兹方程](./docs/zh/examples/lorenz.md) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957) |
| 微分方程 | [若斯叻方程](./docs/zh/examples/rossler.md) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957) |
| 算子学习 | [DeepONet](./docs/zh/examples/deeponet.md) | 数据驱动 | MLP | 监督学习 | [Data](https://deepxde.readthedocs.io/en/latest/demos/operator/antiderivative_unaligned.html) | [Paper](https://export.arxiv.org/pdf/1910.03193.pdf) |
| 微分方程 | [拉普拉斯方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/laplace2d) | 机理驱动 | MLP | 无监督学习 | - | - |
| 微分方程 | [伯格斯方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/deephpms) | 机理驱动 | MLP | 无监督学习 | [Data](https://github.com/maziarraissi/DeepHPMs/tree/master/Data) | [Paper](https://arxiv.org/pdf/1801.06637.pdf) |</center>
| 微分方程 | [非线性偏微分方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/pirbn) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://arxiv.org/abs/2304.06234) |
| 微分方程 | [洛伦兹方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/lorenz) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957) |
| 微分方程 | [若斯叻方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/rossler) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957) |
| 算子学习 | [DeepONet](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/deeponet) | 数据驱动 | MLP | 监督学习 | [Data](https://deepxde.readthedocs.io/en/latest/demos/operator/antiderivative_unaligned.html) | [Paper](https://export.arxiv.org/pdf/1910.03193.pdf) |
| 微分方程 | 梯度增强的物理知识融合PDE求解<sup>coming soon</sup> | 机理驱动 | gPINN | 半监督学习 | - | [Paper](https://www.sciencedirect.com/science/article/abs/pii/S0045782522001438?via%3Dihub) |
| 积分方程 | [沃尔泰拉积分方程](./docs/zh/examples/volterra_ide.md) | 机理驱动 | MLP | 无监督学习 | - | [Project](https://github.com/lululxvi/deepxde/blob/master/examples/pinn_forward/Volterra_IDE.py) |
| 积分方程 | [沃尔泰拉积分方程](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/volterra_ide) | 机理驱动 | MLP | 无监督学习 | - | [Project](https://github.com/lululxvi/deepxde/blob/master/examples/pinn_forward/Volterra_IDE.py) |

<br>
<p align="center"><b>技术科学(AI for Technology)</b></p>

| 问题类型 | 案例名称 | 优化算法 | 模型类型 | 训练方式 | 数据集 | 参考资料 |
|-----|---------|-----|---------|----|---------|---------|
| 定常不可压流体 | [2D 定常方腔流](./docs/zh/examples/ldc2d_steady.md) | 机理驱动 | MLP | 无监督学习 | - | |
| 定常不可压流体 | [2D 达西流](./docs/zh/examples/darcy2d.md) | 机理驱动 | MLP | 无监督学习 | - | |
| 定常不可压流体 | [2D 管道流](./docs/zh/examples/labelfree_DNN_surrogate.md) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://arxiv.org/abs/1906.02382) |
| 定常不可压流体 | [3D 血管瘤](./docs/zh/examples/aneurysm.md) | 机理驱动 | MLP | 无监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/aneurysm/aneurysm_dataset.tar) | [Project](https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/intermediate/adding_stl_files.html)|
| 定常不可压流体 | [任意 2D 几何体绕流](./docs/zh/examples/deepcfd.md) | 数据驱动 | DeepCFD | 监督学习 | - | [Paper](https://arxiv.org/abs/2004.08826)|
| 非定常不可压流体 | [2D 非定常方腔流](./docs/zh/examples/ldc2d_unsteady.md) | 机理驱动 | MLP | 无监督学习 | - | - |
| 非定常不可压流体 | [Re100 2D 圆柱绕流](./docs/zh/examples/cylinder2d_unsteady.md) | 机理驱动 | MLP | 半监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/cylinder2d_unsteady_Re100/cylinder2d_unsteady_Re100_dataset.tar) | [Paper](https://arxiv.org/abs/2004.08826)|
| 非定常不可压流体 | [Re100~750 2D 圆柱绕流](./docs/zh/examples/cylinder2d_unsteady_transformer_physx.md) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957)|
| 可压缩流体 | [2D 空气激波](./docs/zh/examples/shock_wave.md) | 机理驱动 | PINN-WE | 无监督学习 | - | [Paper](https://arxiv.org/abs/2206.03864)|
| 定常不可压流体 | [2D 定常方腔流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/ldc2d_steady) | 机理驱动 | MLP | 无监督学习 | - | |
| 定常不可压流体 | [2D 达西流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/darcy2d) | 机理驱动 | MLP | 无监督学习 | - | |
| 定常不可压流体 | [2D 管道流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/labelfree_DNN_surrogate) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://arxiv.org/abs/1906.02382) |
| 定常不可压流体 | [3D 血管瘤](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/aneurysm) | 机理驱动 | MLP | 无监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/aneurysm/aneurysm_dataset.tar) | [Project](https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/intermediate/adding_stl_files.html)|
| 定常不可压流体 | [任意 2D 几何体绕流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/deepcfd) | 数据驱动 | DeepCFD | 监督学习 | - | [Paper](https://arxiv.org/abs/2004.08826)|
| 非定常不可压流体 | [2D 非定常方腔流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/ldc2d_unsteady) | 机理驱动 | MLP | 无监督学习 | - | - |
| 非定常不可压流体 | [Re100 2D 圆柱绕流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/cylinder2d_unsteady) | 机理驱动 | MLP | 半监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/cylinder2d_unsteady_Re100/cylinder2d_unsteady_Re100_dataset.tar) | [Paper](https://arxiv.org/abs/2004.08826)|
| 非定常不可压流体 | [Re100~750 2D 圆柱绕流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/cylinder2d_unsteady_transformer_physx) | 数据驱动 | Transformer-Physx | 监督学习 | [Data](https://github.com/zabaras/transformer-physx) | [Paper](https://arxiv.org/abs/2010.03957)|
| 可压缩流体 | [2D 空气激波](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/shock_wave) | 机理驱动 | PINN-WE | 无监督学习 | - | [Paper](https://arxiv.org/abs/2206.03864)|
| 飞行器设计 | [MeshGraphNets](https://aistudio.baidu.com/projectdetail/5322713) | 数据驱动 | GNN | 监督学习 | [Data](https://aistudio.baidu.com/datasetdetail/184320) | [Paper](https://arxiv.org/abs/2010.03409)|
| 飞行器设计 | [火箭发动机真空羽流](https://aistudio.baidu.com/projectdetail/4486133) | 数据驱动 | CNN | 监督学习 | [Data](https://aistudio.baidu.com/datasetdetail/167250) | - |
| 飞行器设计 | [Deep-Flow-Prediction](https://aistudio.baidu.com/projectdetail/5671596) | 数据驱动 | TurbNetG | 监督学习 | [Data](https://aistudio.baidu.com/datasetdetail/197778) | [Paper](https://arxiv.org/abs/1810.08217) |
| 流固耦合 | [涡激振动](./docs/zh/examples/viv.md) | 机理驱动 | MLP | 半监督学习 | [Data](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/fsi/VIV_Training_Neta100.mat) | [Paper](https://arxiv.org/abs/2206.03864)|
| 多相流 | [气液两相流](./docs/zh/examples/bubble.md) | 机理驱动 | BubbleNet | 半监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/BubbleNet/bubble.mat) | [Paper](https://pubs.aip.org/aip/adv/article/12/3/035153/2819394/Predicting-micro-bubble-dynamics-with-semi-physics)|
| 流固耦合 | [涡激振动](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/viv) | 机理驱动 | MLP | 半监督学习 | [Data](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/fsi/VIV_Training_Neta100.mat) | [Paper](https://arxiv.org/abs/2206.03864)|
| 多相流 | [气液两相流](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/bubble) | 机理驱动 | BubbleNet | 半监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/BubbleNet/bubble.mat) | [Paper](https://pubs.aip.org/aip/adv/article/12/3/035153/2819394/Predicting-micro-bubble-dynamics-with-semi-physics)|
| 多相流 | [twophasePINN](https://aistudio.baidu.com/projectdetail/5379212) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://doi.org/10.1016/j.mlwa.2021.100029)|
| 多相流 | 非高斯渗透率场估计<sup>coming soon</sup> | 机理驱动 | cINN | 监督学习 | - | [Paper](https://pubs.aip.org/aip/adv/article/12/3/035153/2819394/Predicting-micro-bubble-dynamics-with-semi-physics)|
| 流场高分辨率重构 | [2D 湍流流场重构](./docs/zh/examples/tempoGAN.md) | 数据驱动 | tempoGAN | 监督学习 | [Train Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_train.mat)<br>[Eval Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_valid.mat) | [Paper](https://dl.acm.org/doi/10.1145/3197517.3201304)|
| 流场高分辨率重构 | [2D 湍流流场重构](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/tempoGAN) | 数据驱动 | tempoGAN | 监督学习 | [Train Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_train.mat)<br>[Eval Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_valid.mat) | [Paper](https://dl.acm.org/doi/10.1145/3197517.3201304)|
| 流场高分辨率重构 | [2D 湍流流场重构](https://aistudio.baidu.com/projectdetail/4493261?contributionType=1) | 数据驱动 | cycleGAN | 监督学习 | [Train Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_train.mat)<br>[Eval Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/tempoGAN/2d_valid.mat) | [Paper](https://arxiv.org/abs/2007.15324)|
| 流场高分辨率重构 | [基于Voronoi嵌入辅助深度学习的稀疏传感器全局场重建](https://aistudio.baidu.com/projectdetail/5807904) | 数据驱动 | CNN | 监督学习 | [Data1](https://drive.google.com/drive/folders/1K7upSyHAIVtsyNAqe6P8TY1nS5WpxJ2c)<br>[Data2](https://drive.google.com/drive/folders/1pVW4epkeHkT2WHZB7Dym5IURcfOP4cXu)<br>[Data3](https://drive.google.com/drive/folders/1xIY_jIu-hNcRY-TTf4oYX1Xg4_fx8ZvD) | [Paper](https://arxiv.org/pdf/2202.11214.pdf) |
| 流场高分辨率重构 | 基于扩散的流体超分重构<sup>coming soon</sup> | 数理融合 | DDPM | 监督学习 | - | [Paper](https://www.sciencedirect.com/science/article/pii/S0021999123000670)|
| 求解器耦合 | [CFD-GCN](./docs/zh/examples/cfdgcn.md) | 数据驱动 | GCN | 监督学习 | [Data](https://aistudio.baidu.com/aistudio/datasetdetail/184778)<br>[Mesh](https://paddle-org.bj.bcebos.com/paddlescience/datasets/CFDGCN/meshes.tar) | [Paper](https://arxiv.org/abs/2007.04439)|
| 求解器耦合 | [CFD-GCN](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/cfdgcn) | 数据驱动 | GCN | 监督学习 | [Data](https://aistudio.baidu.com/aistudio/datasetdetail/184778)<br>[Mesh](https://paddle-org.bj.bcebos.com/paddlescience/datasets/CFDGCN/meshes.tar) | [Paper](https://arxiv.org/abs/2007.04439)|
| 受力分析 | [1D 欧拉梁变形](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/euler_beam/euler_beam.py) | 机理驱动 | MLP | 无监督学习 | - | - |
| 受力分析 | [2D 平板变形](https://aistudio.baidu.com/aistudio/projectdetail/5792325) | 机理驱动 | MLP | 无监督学习 | - | - |
| 受力分析 | [3D 连接件变形](./docs/zh/examples/bracket.md) | 机理驱动 | MLP | 无监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/bracket/bracket_dataset.tar) | [Tutorial](https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/foundational/linear_elasticity.html) |
| 受力分析 | [结构震动模拟](./docs/zh/examples/phylstm.md) | 机理驱动 | PhyLSTM | 监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/PhyLSTM/data_boucwen.mat) | [Paper](https://arxiv.org/abs/2002.10253) |
| 受力分析 | [3D 连接件变形](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/bracket) | 机理驱动 | MLP | 无监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/bracket/bracket_dataset.tar) | [Tutorial](https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/foundational/linear_elasticity.html) |
| 受力分析 | [结构震动模拟](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/phylstm) | 机理驱动 | PhyLSTM | 监督学习 | [Data](https://paddle-org.bj.bcebos.com/paddlescience/datasets/PhyLSTM/data_boucwen.mat) | [Paper](https://arxiv.org/abs/2002.10253) |

<br>
<p align="center"><b>材料科学(AI for Material)</b></p>
Expand All @@ -78,7 +78,7 @@ PaddleScience 是一个基于深度学习框架 PaddlePaddle 开发的科学计

| 问题类型 | 案例名称 | 优化算法 | 模型类型 | 训练方式 | 数据集 | 参考资料 |
|-----|---------|-----|---------|----|---------|---------|
| 天气预报 | [FourCastNet 气象预报](./docs/zh/examples/fourcastnet.md) | 数据驱动 | FourCastNet | 监督学习 | [ERA5](https://app.globus.org/file-manager?origin_id=945b3c9e-0f8c-11ed-8daf-9f359c660fbd&origin_path=%2F~%2Fdata%2F) | [Paper](https://arxiv.org/pdf/2202.11214.pdf) |
| 天气预报 | [FourCastNet 气象预报](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/fourcastnet) | 数据驱动 | FourCastNet | 监督学习 | [ERA5](https://app.globus.org/file-manager?origin_id=945b3c9e-0f8c-11ed-8daf-9f359c660fbd&origin_path=%2F~%2Fdata%2F) | [Paper](https://arxiv.org/pdf/2202.11214.pdf) |
| 天气预报 | GraphCast 气象预报<sup>coming soon</sup> | 数据驱动 | GraphCastNet* | 监督学习 | - | [Paper](https://arxiv.org/pdf/2202.11214.pdf) |
| 大气污染物 | [UNet 污染物扩散](https://aistudio.baidu.com/projectdetail/5663515?channel=0&channelType=0&sUid=438690&shared=1&ts=1698221963752) | 数据驱动 | UNet | 监督学习 | [Data](https://aistudio.baidu.com/datasetdetail/198102) | - |

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10 changes: 10 additions & 0 deletions docs/zh/examples/laplace2d.md
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Expand Up @@ -8,6 +8,16 @@
python laplace2d.py
```

=== "模型评估命令"

``` sh
python laplace2d.py mode=eval EVAL.pretrained_model_path=https://paddle-org.bj.bcebos.com/paddlescience/models/laplace2d/laplace2d_pretrained.pdparams
```

| 预训练模型 | 指标 |
|:--| :--|
| [laplace2d_pretrained.pdparams](https://paddle-org.bj.bcebos.com/paddlescience/models/laplace2d/laplace2d_pretrained.pdparams) | loss(MSE_Metric): 0.00002<br>MSE.u(MSE_Metric): 0.00002 |

## 1. 背景简介

拉普拉斯方程由法国数学家拉普拉斯首先提出而得名，该方程在许多领域都有重要应用，例如电磁学、天文学和流体力学等。在实际应用中，拉普拉斯方程的求解往往是一个复杂的数学问题。对于一些具有特定边界条件和初始条件的实际问题，可以通过特定的数值方法（如有限元方法、有限差分方法等）来求解拉普拉斯方程。对于一些复杂的问题，可能需要采用更高级的数值方法或者借助高性能计算机进行计算。
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4 changes: 2 additions & 2 deletions examples/bracket/bracket.py
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Expand Up @@ -521,9 +521,9 @@ def evaluate(cfg: DictConfig):
pretrained_model_path=cfg.EVAL.pretrained_model_path,
eval_with_no_grad=cfg.EVAL.eval_with_no_grad,
)
# evaluate after finished training
# evaluate
solver.eval()
# visualize prediction after finished training
# visualize prediction
solver.visualize()


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2 changes: 1 addition & 1 deletion examples/bubble/bubble.py
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Expand Up @@ -356,7 +356,7 @@ def transform_out(in_, out):
)
solver.eval()

# visualize prediction after finished training
# visualize prediction
visu_mat = geom["time_rect_visu"].sample_interior(
NPOINT_PDE * NTIME_PDE, evenly=True
)
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2 changes: 1 addition & 1 deletion examples/deepcfd/deepcfd.py
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Expand Up @@ -446,7 +446,7 @@ def metric_expr(
PLOT_DIR = os.path.join(cfg.output_dir, "visual")
os.makedirs(PLOT_DIR, exist_ok=True)

# visualize prediction after finished training
# visualize prediction
predict_and_save_plot(test_x, test_y, 0, solver, PLOT_DIR)


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2 changes: 1 addition & 1 deletion examples/epnn/epnn.py
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Expand Up @@ -187,7 +187,7 @@ def transform_f_stress(_in):
pretrained_model_path=cfg.EVAL.pretrained_model_path,
eval_with_no_grad=cfg.EVAL.eval_with_no_grad,
)
# evaluate after finished training
# evaluate
solver.eval()


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4 changes: 2 additions & 2 deletions examples/hpinns/holography.py
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Expand Up @@ -271,7 +271,7 @@ def train(cfg: DictConfig):

# train model
solver.train()
# evaluate after finished training
# evaluate
solver.eval()
# append objective loss for plot
loss_log_obj.append(func_module.loss_obj)
Expand Down Expand Up @@ -405,7 +405,7 @@ def evaluate(cfg: DictConfig):
pretrained_model_path=cfg.EVAL.pretrained_model_path,
)

# evaluate after finished training
# evaluate
solver.eval()


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2 changes: 1 addition & 1 deletion examples/laplace/laplace2d.py
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Expand Up @@ -201,7 +201,7 @@ def u_solution_func(out):
pretrained_model_path=cfg.EVAL.pretrained_model_path,
)
solver.eval()
# visualize prediction after finished training
# visualize prediction
solver.visualize()


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2 changes: 1 addition & 1 deletion examples/phylstm/phylstm2.py
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Expand Up @@ -302,7 +302,7 @@ def evaluate(cfg: DictConfig):
pretrained_model_path=cfg.EVAL.pretrained_model_path,
eval_with_no_grad=cfg.EVAL.eval_with_no_grad,
)
# evaluate after finished training
# evaluate
solver.eval()


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2 changes: 1 addition & 1 deletion examples/phylstm/phylstm3.py
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Expand Up @@ -321,7 +321,7 @@ def evaluate(cfg: DictConfig):
eval_with_no_grad=cfg.EVAL.eval_with_no_grad,
)

# evaluate after finished training
# evaluate
solver.eval()


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