"""Backend supported: tensorflow.compat.v1, tensorflow, pytorch, paddle""" import deepxde as dde def pde(x, y): dy_r = dde.grad.jacobian(y, x, i=0, j=0) return dy_r + x[:, 0:1] def solution(X): r, x = X[:, 0:1], X[:, 1:] return 4 - r ** 2 def boundary(x, on_boundary): return on_boundary geom = dde.geometry.Rectangle(xmin=[-2, 0], xmax=[2, 20]) bc = dde.DirichletBC(geom, solution, boundary) data = dde.data.PDE(geom, pde, bc, 1600, 200, solution=solution, num_test=1000) net = dde.maps.FNN([2] + [20] * 3 + [1], "tanh", "Glorot normal") model = dde.Model(data, net) model.compile("adam", lr=0.01, metrics=["l2 relative error"]) losshistory, train_state = model.train(epochs=1500) dde.saveplot(losshistory, train_state, issave=True, isplot=True)

这段代码是用于求解一个二维偏微分方程的。其中，使用了深度学习库deepxde来实现求解过程。具体来说，这个方程是一个二阶常微分方程，可以使用dde.grad.jacobian函数求取其导数。模型使用了一个三层的前馈神经网络，并使用adam优化算法进行训练。最终的训练结果保存在losshistory和train_state中，并可通过dde.saveplot函数进行可视化。

相关问题

请对以下代码进行更改，使其可以输出流场图"""Backend supported: tensorflow.compat.v1, tensorflow, pytorch, paddle""" import deepxde as dde def pde(x, y): dy_r = dde.grad.jacobian(y, x, i=0, j=0) return dy_r + x[:, 0:1] def solution(X): r, x = X[:, 0:1], X[:, 1:] return 4 - r ** 2 def boundary(x, on_boundary): return on_boundary geom = dde.geometry.Rectangle(xmin=[-2, 0], xmax=[2, 20]) bc = dde.DirichletBC(geom, solution, boundary) data = dde.data.PDE(geom, pde, bc, 1600, 200, solution=solution, num_test=1000) net = dde.maps.FNN([2] + [20] * 3 + [1], "tanh", "Glorot normal") model = dde.Model(data, net) model.compile("adam", lr=0.01, metrics=["l2 relative error"]) losshistory, train_state = model.train(epochs=1500) dde.saveplot(losshistory, train_state, issave=True, isplot=True)

为了输出流场图，我们需要修改代码如下：

import numpy as np
import matplotlib.pyplot as plt

# 计算解析解
def exact_solution(x):
    r, x = x[:, 0:1], x[:, 1:]
    return 2 * (1 - np.exp(-r**2 / 4)) - x**2 / 2

# 生成网格
X, Y = np.meshgrid(np.linspace(-2, 2, 100), np.linspace(0, 20, 100))
XY = np.hstack((X.flatten()[:, None], Y.flatten()[:, None]))

# 计算模型预测值
prediction = model.predict(XY)
Z = prediction.reshape(100, 100)

# 绘制流场图
plt.figure()
plt.contourf(X, Y, Z, levels=20, cmap=plt.cm.jet)
plt.colorbar()
plt.xlabel("x")
plt.ylabel("y")
plt.title("Flow field")
plt.show()

我们首先定义了一个exact_solution函数，用于计算解析解。然后创建一个100x100的网格，并使用model.predict函数计算模型的预测值，最终通过plt.contourf函数绘制流场图。

AttributeError: module 'tensorflow.compat.v2.__internal__' has no attribute 'register_clear_session_function'

This error occurs when trying to use the `register_clear_session_function` function from the `tensorflow.compat.v2.__internal__` module. This function is no longer available in TensorFlow 2.x, and has been removed to simplify the API.

To fix this error, you can remove the calls to `register_clear_session_function` from your code. If you need to clear the TensorFlow session, you can use the `tf.keras.backend.clear_session()` function instead.