TensorFlow生成图实例详解

偏微分方程(PDE)是微分方程的主要类型, 它涉及具有多个自变量的未知函数的偏导数。关于偏微分方程, 我们专注于创建新图。

让我们假设有一个尺寸为500 * 500平方英寸的池塘-

N = 500

现在, 我们将计算偏微分方程并使用它形成相应的图。生成下面给出的计算图形的步骤。

在TensorFlow代码中将v1升级到v2的操作如下：

import tensorflow.compat.v1 as tf tf.disable_v2_behavior()

步骤1-首先, 导入库进行仿真。

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

步骤2-包含用于将2D数组转换为卷积核的函数, 并简化成形图的2D卷积操作。

例：

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, j): ""2D convolutional operation is generated below"": x = tf.expand_dims(tf.expand_dims(x, 0), -1) y = tf.nn.depthwise_conv2d(x, j, [1, 1, 1, 1], padding = 'SAME') return y[0, :, :, 0] def laplace(x): """Computing 2D laplacian of the arrays""": laplace_j = make_kernel ([[0.5, 1.0, 0.5], [1.0, -6., 1.0], [0.5, 1.0, 0.5]]) return simple_conv(x, laplace_j) sess = tf.InteractiveSession() We are going to step 3 now.

步骤3-包括迭代次数并计算图以相应地显示记录：-

N = 500 # Initial Conditions -- some raindrops hit the pond: # Setting the zero here: u_init = np.zeros([N, N], dtype = np.float32) ut_init = np.zeros([N, N], dtype = np.float32) #Few rain drops hit a pond at random points: 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() # Parameters of Graphs # eps -- time resolution # damping -- wave damping eps = tf.placeholder(tf.float32, shape = ()) damping = tf.placeholder(tf.float32, shape = ()) # Creating variable for simulation state U = tf.Variable(u_init) Ut = tf.Variable(ut_init) # Discretized PDE updated rule: U_ = U + eps * Ut Ut_ = Ut + eps*(laplace(U) - damping * Ut) # Updating the state of rules: step =tf.group(U.assign(U_), Ut.assign(Ut_)) # Initializing state to initial conditions tf.initialize_all_variables().run() # Running 1000 steps of PDE and forming graph for i in range(1000): # Step simulating: step.run({eps: 0.03, damping: 0.04}) # Visualizing every 50 steps if i % 500 == 0: plt.imshow(U.eval()) plt.show()

输出