/**/

# TensorFlow - 形成图

N=500

```import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt```

```def make_kernel(a):
a=np.asarray(a)
a=a.reshape(list(a.shape) + [1,1])
return tf.constant(a, dtype=1)

def simple_conv(x, k):
"""A simplified 2D convolution operation"""
x=tf.expand_dims(tf.expand_dims(x, 0), -1)
y=tf.nn.depthwise_conv2d(x, k, [1, 1, 1, 1], padding='SAME')
return y[0, :, :, 0]

def laplace(x):
"""Compute the 2D laplacian of an array"""
laplace_k=make_kernel([[0.5, 1.0, 0.5], [1.0, -6., 1.0], [0.5, 1.0, 0.5]])
return simple_conv(x, laplace_k)

sess=tf.InteractiveSession()```

```N=500

# 初始条件 - 有些雨滴击中了一个池塘

# 将所有东西设置为零
u_init=np.zeros([N, N], dtype=np.float32)
ut_init=np.zeros([N, N], dtype=np.float32)

# 一些雨滴在随机点击中了一个池塘
for n in range(100):
a,b=np.random.randint(0, N, 2)
u_init[a,b]=np.random.uniform()

plt.imshow(u_init)
plt.show()

# 参数：
# eps -- time resolution
# damping -- wave damping
eps=tf.placeholder(tf.float32, shape=())
damping=tf.placeholder(tf.float32, shape=())

# 为仿真状态创建变量
U=tf.Variable(u_init)
Ut=tf.Variable(ut_init)

# 离散的PDE更新规则
U_=U + eps * Ut
Ut_=Ut + eps * (laplace(U) - damping * Ut)

# 操作更新状态
step=tf.group(U.assign(U_), Ut.assign(Ut_))

# 将状态初始化为初始条件
tf.initialize_all_variables().run()

# 运行1000步PDE
for i in range(1000):
# 步骤仿真
step.run({eps: 0.03, damping: 0.04})

# 每50个步骤可视化
if i % 500 == 0:
plt.imshow(U.eval())
plt.show()```

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