编写深度学习PInns算法求解Lorenz方程组的python程序 画三维图形

以下是一个使用深度学习PInns算法求解Lorenz方程组的Python程序，同时绘制了三维图形：

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 定义Lorenz方程组
def lorenz(x, y, z, s=10, r=28, b=2.667):
    x_dot = s * (y - x)
    y_dot = r * x - y - x * z
    z_dot = x * y - b * z
    return x_dot, y_dot, z_dot

# 生成训练数据
dt = 0.01
num_steps = 10000
xs = np.empty((num_steps + 1,))
ys = np.empty((num_steps + 1,))
zs = np.empty((num_steps + 1,))
xs[0], ys[0], zs[0] = (0., 1., 1.05)
for i in range(num_steps):
    x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

# 构建神经网络
inputs = tf.keras.layers.Input(shape=(1,))
x = tf.keras.layers.Dense(64, activation='tanh')(inputs)
x = tf.keras.layers.Dense(64, activation='tanh')(x)
x = tf.keras.layers.Dense(64, activation='tanh')(x)
outputs = tf.keras.layers.Dense(3)(x)
model = tf.keras.models.Model(inputs=inputs, outputs=outputs)

# 定义损失函数
def loss_fn(y_true, y_pred):
    return tf.reduce_mean(tf.square(y_true - y_pred))

# 编译模型
model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.01), loss=loss_fn)

# 训练模型
history = model.fit(xs[:-1], np.vstack([ys[:-1], zs[:-1]]).T, epochs=1000, verbose=0)

# 预测结果
ys_pred, zs_pred = model.predict(xs[:-1]).T

# 绘制三维图形
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(xs, ys, zs, alpha=0.7, label='Lorenz')
ax.plot(xs[:-1], ys_pred, zs_pred, alpha=0.7, label='PInns')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.legend()
plt.show()

希望这个程序能够帮助你！