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‎README.md

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@@ -26,14 +26,16 @@ PaddleScience 是一个基于深度学习框架 PaddlePaddle 开发的科学计
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| 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 |
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|-----|---------|-----|---------|----|---------|---------|
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| 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 | - | - |
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| 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>
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| 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) |
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| 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 | PIRBN | 无监督学习 | - | [Paper](https://arxiv.org/abs/2304.06234) |
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| 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) |
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| 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) |
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| 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) |
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| 微分方程 | [梯度增强的物理知识融合 PDE 求解](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/gpinn/poisson_1d.py) | 机理驱动 | gPINN | 无监督学习 | - | [Paper](https://doi.org/10.1016/j.cma.2022.114823) |
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| 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) |
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| 微分方程 | [分数阶微分方程](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/fpde/fractional_poisson_2d.py) | 机理驱动 | MLP | 无监督学习 | - | - |
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| 光孤子 | [Optical soliton](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/nlsmb) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://doi.org/10.1007/s11071-023-08824-w)|
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| 光纤怪波 | [Optical rogue wave](https://paddlescience-docs.readthedocs.io/zh/latest/zh/examples/nlsmb) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://doi.org/10.1007/s11071-023-08824-w)|
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<br>
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<p align="center"><b>技术科学(AI for Technology)</b></p>

‎docs/index.md

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| 微分方程 | [梯度增强的物理知识融合 PDE 求解](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/gpinn/poisson_1d.py) | 机理驱动 | gPINN | 无监督学习 | - | [Paper](https://doi.org/10.1016/j.cma.2022.114823) |
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| 积分方程 | [沃尔泰拉积分方程](./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) |
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| 微分方程 | [分数阶微分方程](https://github.com/PaddlePaddle/PaddleScience/blob/develop/examples/fpde/fractional_poisson_2d.py) | 机理驱动 | MLP | 无监督学习 | - | - |
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| 光孤子 | [Optical soliton](./zh/examples/nlsmb.md) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://doi.org/10.1007/s11071-023-08824-w)|
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| 光纤怪波 | [Optical rogue wave](./zh/examples/nlsmb.md) | 机理驱动 | MLP | 无监督学习 | - | [Paper](https://doi.org/10.1007/s11071-023-08824-w)|
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<br>
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<p align="center"><b>技术科学(AI for Technology)</b></p>

‎docs/zh/examples/biharmonic2d.md

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python biharmonic2d.py mode=eval EVAL.pretrained_model_path=https://paddle-org.bj.bcebos.com/paddlescience/models/biharmonic2d/biharmonic2d_pretrained.pdparams
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```
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=== "模型导出命令"
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``` sh
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python biharmonic2d.py mode=export
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```
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=== "模型推理命令"
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``` sh
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python biharmonic2d.py mode=infer
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```
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| 预训练模型 | 指标 |
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|:--| :--|
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| [biharmonic2d_pretrained.pdparams](https://paddle-org.bj.bcebos.com/paddlescience/models/biharmonic2d/biharmonic2d_pretrained.pdparams) | l2_error: 0.02774 |

‎docs/zh/examples/nlsmb.md

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| 预训练模型 | 指标 |
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|:--| :--|
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| [NLS-MB_soliton_pretrained.pdparams](https://paddle-org.bj.bcebos.com/paddlescience/models/NLS-MB/NLS-MB_soliton_pretrained.pdparams) | loss(Residual): 0.00007<br>MSE.Schrodinger_1(Residual): 0.00002<br>MSE.Schrodinger_2(Residual): 0.00002<br>MSE.Maxwell_1(Residual): 0.00001<br>MSE.Maxwell_2(Residual): 0.00001<br>MSE.Bloch(Residual): 0.00001 |
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| [NLS-MB_soliton_pretrained.pdparams](https://paddle-org.bj.bcebos.com/paddlescience/models/NLS-MB/NLS-MB_soliton_pretrained.pdparams) | Residual/loss: 0.00000<br>Residual/MSE.Schrodinger_1: 0.00000<br>Residual/MSE.Schrodinger_2: 0.00000<br>Residual/MSE.Maxwell_1: 0.00000<br>Residual/MSE.Maxwell_2: 0.00000<br>Residual/MSE.Bloch: 0.00000 |
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| [NLS-MB_optical_rogue_wave.pdparams](https://paddle-org.bj.bcebos.com/paddlescience/models/NLS-MB/NLS-MB_optical_rogue_wave.pdparams) | Residual/loss: 0.00001<br>Residual/MSE.Schrodinger_1: 0.00000<br>Residual/MSE.Schrodinger_2: 0.00000<br>Residual/MSE.Maxwell_1: 0.00000<br>Residual/MSE.Maxwell_2: 0.00000<br>Residual/MSE.Bloch: 0.00000 |
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## 1. 背景简介
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<figure markdown>
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![optical_soliton](https://paddle-org.bj.bcebos.com/paddlescience/docs/NLS-MB/pred_optical_soliton.png){ loading=lazy}
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<figcaption>解析解结果与 PINN 预测结果对比，从上到下分别为：慢变电场（E），共振偏量（p）以及粒子数反转程度（$\eta$）</figcaption>
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<figcaption>解析解结果与 PINN 预测结果对比，从上到下分别为：慢变电场（E），共振偏量（p）以及粒子数反转程度（eta）</figcaption>
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</figure>
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### 5.2 optical_rogue_wave
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<figure markdown>
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![optical_rogue_wave](https://paddle-org.bj.bcebos.com/paddlescience/docs/NLS-MB/pred_optical_rogue_wave.png){ loading=lazy}
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<figcaption>解析解结果与 PINN 预测结果对比，从上到下分别为：慢变电场（E），共振偏量（p）以及粒子数反转程度（$\eta$）</figcaption>
249+
<figcaption>解析解结果与 PINN 预测结果对比，从上到下分别为：慢变电场（E），共振偏量（p）以及粒子数反转程度（eta）</figcaption>
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</figure>
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可以看到PINN预测与解析解的结果基本一致。
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## 6. 参考资料
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[1] [S.-Y. Xu, Q. Zhou, and W. Liu, Prediction of Soliton Evolution and Equation Parameters for NLS–MB Equation Based on the phPINN Algorithm, Nonlinear Dyn (2023)](https://doi.org/10.1007/s11071-023-08824-w).
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[1] [S.-Y. Xu, Q. Zhou, and W. Liu, Prediction of Soliton Evolution and Equation Parameters for NLS–MB Equation Based on the phPINN Algorithm, Nonlinear Dyn (2023)](https://doi.org/10.1007/s11071-023-08824-w).

‎examples/NLS-MB/NLS-MB_optical_rogue_wave.py

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def analytic_solution(out):
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I = 1j
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x = out["x"]
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t = out["t"]
29+
x = out["x"]
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EExact = (
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(-1565 * x**2 + (648 * I + 76 * t) * x - 68 * t**2 + 51)
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* np.exp(-I / 8 * (-12 * t + 65 * x))
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idx_ub = np.random.choice(np.where(ub)[0], 200, replace=False)
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icbc_idx = np.hstack((idx_lb, idx_ic, idx_ub))
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X_u_train = X_star[icbc_idx].astype("float32")
152-
X_u_train = {"x": X_u_train[:, 0:1], "t": X_u_train[:, 1:2]}
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X_u_train = {"t": X_u_train[:, 1:2], "x": X_u_train[:, 0:1]}
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Eu_train, Ev_train, pu_train, pv_train, eta_train = analytic_solution(X_u_train)
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train_dataloader_cfg = {
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"dataset": {
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"name": "NamedArrayDataset",
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"input": {"x": X_u_train["x"], "t": X_u_train["t"]},
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"input": {"t": X_u_train["t"], "x": X_u_train["x"]},
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"label": {
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"Eu": Eu_train,
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"Ev": Ev_train,
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vis_points = geom["time_interval"].sample_interior(20000, evenly=True)
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Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(vis_points)
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pred = solver.predict(vis_points, return_numpy=True)
281-
x = vis_points["x"][:, 0]
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t = vis_points["t"][:, 0]
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x = vis_points["x"][:, 0]
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E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
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E_pred = np.sqrt(pred["Eu"] ** 2 + pred["Ev"] ** 2)[:, 0]
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p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]
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vis_points = geom["time_interval"].sample_interior(20000, evenly=True)
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Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(vis_points)
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pred = solver.predict(vis_points, return_numpy=True)
357-
x = vis_points["x"][:, 0]
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t = vis_points["t"][:, 0]
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x = vis_points["x"][:, 0]
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E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
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E_pred = np.sqrt(pred["Eu"] ** 2 + pred["Ev"] ** 2)[:, 0]
361361
p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]
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417417
store_key: output_dict[infer_key]
418418
for store_key, infer_key in zip(cfg.MODEL.output_keys, output_dict.keys())
419419
}
420+
# TODO: Fix this mapping diff in dy2st
421+
(
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output_dict["Eu"],
423+
output_dict["Ev"],
424+
output_dict["eta"],
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output_dict["pu"],
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output_dict["pv"],
427+
) = (
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output_dict["Eu"],
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output_dict["Ev"],
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output_dict["pu"],
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output_dict["pv"],
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output_dict["eta"],
433+
)
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# visualize prediction
422436
Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(input_dict)
423-
x = input_dict["x"][:, 0]
424437
t = input_dict["t"][:, 0]
438+
x = input_dict["x"][:, 0]
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E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
426440
E_pred = np.sqrt(output_dict["Eu"] ** 2 + output_dict["Ev"] ** 2)[:, 0]
427441
p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]

‎examples/NLS-MB/NLS-MB_optical_soliton.py

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def analytic_solution(out):
27-
x, t = out["x"], out["t"]
27+
t, x = out["t"], out["x"]
2828
Eu_true = 2 * np.cos(2 * t) / np.cosh(2 * t + 6 * x)
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Ev_true = -2 * np.sin(2 * t) / np.cosh(2 * t + 6 * x)
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8383
plt.subplot(3, 3, 9)
8484
plt.title("eta_diff")
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plt.tricontourf(x, t, np.abs(eta_ref - eta_pred), levels=256, cmap="jet")
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fig_path = osp.join(output_dir, "pred_optical_soliton.png")
8887
print(f"Saving figure to {fig_path}")
8988
fig.savefig(fig_path, bbox_inches="tight", dpi=400)
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127126
idx_ub = np.random.choice(np.where(ub)[0], 200, replace=False)
128127
icbc_idx = np.hstack((idx_lb, idx_ic, idx_ub))
129128
X_u_train = X_star[icbc_idx].astype("float32")
130-
X_u_train = {"x": X_u_train[:, 0:1], "t": X_u_train[:, 1:2]}
129+
X_u_train = {"t": X_u_train[:, 1:2], "x": X_u_train[:, 0:1]}
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Eu_train, Ev_train, pu_train, pv_train, eta_train = analytic_solution(X_u_train)
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train_dataloader_cfg = {
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"dataset": {
136135
"name": "NamedArrayDataset",
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"input": {"x": X_u_train["x"], "t": X_u_train["t"]},
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"input": {"t": X_u_train["t"], "x": X_u_train["x"]},
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"label": {
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"Eu": Eu_train,
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"Ev": Ev_train,
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256255
vis_points = geom["time_interval"].sample_interior(20000, evenly=True)
257256
Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(vis_points)
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pred = solver.predict(vis_points, return_numpy=True)
259-
x = vis_points["x"][:, 0]
260258
t = vis_points["t"][:, 0]
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x = vis_points["x"][:, 0]
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E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
262261
E_pred = np.sqrt(pred["Eu"] ** 2 + pred["Ev"] ** 2)[:, 0]
263262
p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]
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332331
vis_points = geom["time_interval"].sample_interior(20000, evenly=True)
333332
Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(vis_points)
334333
pred = solver.predict(vis_points, return_numpy=True)
335-
x = vis_points["x"][:, 0]
336334
t = vis_points["t"][:, 0]
335+
x = vis_points["x"][:, 0]
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E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
338337
E_pred = np.sqrt(pred["Eu"] ** 2 + pred["Ev"] ** 2)[:, 0]
339338
p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]
@@ -395,11 +394,25 @@ def inference(cfg: DictConfig):
395394
store_key: output_dict[infer_key]
396395
for store_key, infer_key in zip(cfg.MODEL.output_keys, output_dict.keys())
397396
}
397+
# TODO: Fix this mapping diff in dy2st
398+
(
399+
output_dict["Eu"],
400+
output_dict["Ev"],
401+
output_dict["eta"],
402+
output_dict["pu"],
403+
output_dict["pv"],
404+
) = (
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output_dict["Eu"],
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output_dict["Ev"],
407+
output_dict["pu"],
408+
output_dict["pv"],
409+
output_dict["eta"],
410+
)
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399412
# visualize prediction
400413
Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(input_dict)
401-
x = input_dict["x"][:, 0]
402414
t = input_dict["t"][:, 0]
415+
x = input_dict["x"][:, 0]
403416
E_ref = np.sqrt(Eu_true**2 + Ev_true**2)[:, 0]
404417
E_pred = np.sqrt(output_dict["Eu"] ** 2 + output_dict["Ev"] ** 2)[:, 0]
405418
p_ref = np.sqrt(pu_true**2 + pv_true**2)[:, 0]

‎examples/NLS-MB/conf/NLS-MB_rogue_wave.yaml

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# general settings
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mode: train # running mode: train/eval
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seed: 42
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log_freq: 20
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log_freq: 100
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output_dir: ${hydra:run.dir}
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NPOINT_INTERIOR: 20000
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NPOINT_BC: 600
3232
NTIME_ALL: 200
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# model settings
3635
MODEL:
37-
input_keys: ["x", "t"]
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input_keys: ["t", "x"]
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output_keys: ["Eu", "Ev", "pu", "pv", "eta"]
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num_layers: 5
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hidden_size: 64
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5756
# evaluation settings
5857
EVAL:
5958
pretrained_model_path: null
60-
eval_with_no_grad: true
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eval_with_no_grad: false
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INFER:
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pretrained_model_path: https://paddle-org.bj.bcebos.com/paddlescience/models/NLS-MB/NLS-MB_rogue_wave_pretrained.pdparams

‎examples/NLS-MB/conf/NLS-MB_soliton.yaml

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# general settings
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mode: train # running mode: train/eval
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seed: 42
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log_freq: 20
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log_freq: 100
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output_dir: ${hydra:run.dir}
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NPOINT_INTERIOR: 20000
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NPOINT_BC: 600
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NTIME_ALL: 200
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# model settings
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MODEL:
36-
input_keys: ["x", "t"]
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input_keys: ["t", "x"]
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output_keys: ["Eu", "Ev", "pu", "pv", "eta"]
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num_layers: 5
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hidden_size: 64
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# evaluation settings
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EVAL:
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pretrained_model_path: null
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eval_with_no_grad: true
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eval_with_no_grad: false
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INFER:
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pretrained_model_path: https://paddle-org.bj.bcebos.com/paddlescience/models/NLS-MB/NLS-MB_soliton_pretrained.pdparams

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