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[Fix] Fix NLS-MB document and code (#859)
* execute 'ldconfig' after /bin/bash automatically * add_dockerhub * refine doc * update base image to paddle official image(test=document_fix) * Fix NLS-MB examples code and document
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‎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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@@ -238,18 +239,18 @@ examples/NLS-MB/NLS-MB_optical_soliton.py
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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>
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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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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"]
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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")
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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)
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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)
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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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store_key: output_dict[infer_key]
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for store_key, infer_key in zip(cfg.MODEL.output_keys, output_dict.keys())
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}
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# TODO: Fix this mapping diff in dy2st
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(
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output_dict["Eu"],
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output_dict["Ev"],
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output_dict["eta"],
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output_dict["pu"],
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output_dict["pv"],
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) = (
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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"],
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)
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# visualize prediction
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Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(input_dict)
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x = input_dict["x"][:, 0]
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t = input_dict["t"][:, 0]
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x = input_dict["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(output_dict["Eu"] ** 2 + output_dict["Ev"] ** 2)[:, 0]
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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):
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x, t = out["x"], out["t"]
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t, x = out["t"], out["x"]
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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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plt.subplot(3, 3, 9)
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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")
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print(f"Saving figure to {fig_path}")
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fig.savefig(fig_path, bbox_inches="tight", dpi=400)
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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")
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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)
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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)
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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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store_key: output_dict[infer_key]
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for store_key, infer_key in zip(cfg.MODEL.output_keys, output_dict.keys())
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}
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# TODO: Fix this mapping diff in dy2st
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(
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output_dict["Eu"],
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output_dict["Ev"],
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output_dict["eta"],
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output_dict["pu"],
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output_dict["pv"],
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) = (
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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"],
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)
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# visualize prediction
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Eu_true, Ev_true, pu_true, pv_true, eta_true = analytic_solution(input_dict)
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x = input_dict["x"][:, 0]
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t = input_dict["t"][:, 0]
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x = input_dict["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(output_dict["Eu"] ** 2 + output_dict["Ev"] ** 2)[:, 0]
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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
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NTIME_ALL: 200
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# model settings
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MODEL:
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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_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:
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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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