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diff --git a/tensorflow/docs_src/tutorials/non-ml/pdes.md b/tensorflow/docs_src/tutorials/non-ml/pdes.md deleted file mode 100644 index b5a0fa834a..0000000000 --- a/tensorflow/docs_src/tutorials/non-ml/pdes.md +++ /dev/null @@ -1,140 +0,0 @@ -# Partial Differential Equations - -TensorFlow isn't just for machine learning. Here we give a (somewhat -pedestrian) example of using TensorFlow for simulating the behavior of a -[partial differential equation]( -https://en.wikipedia.org/wiki/Partial_differential_equation). -We'll simulate the surface of square pond as a few raindrops land on it. - - -## Basic Setup - -A few imports we'll need. - -```python -#Import libraries for simulation -import tensorflow as tf -import numpy as np - -#Imports for visualization -import PIL.Image -from io import BytesIO -from IPython.display import clear_output, Image, display -``` - -A function for displaying the state of the pond's surface as an image. - -```python -def DisplayArray(a, fmt='jpeg', rng=[0,1]): - """Display an array as a picture.""" - a = (a - rng[0])/float(rng[1] - rng[0])*255 - a = np.uint8(np.clip(a, 0, 255)) - f = BytesIO() - PIL.Image.fromarray(a).save(f, fmt) - clear_output(wait = True) - display(Image(data=f.getvalue())) -``` - -Here we start an interactive TensorFlow session for convenience in playing -around. A regular session would work as well if we were doing this in an -executable .py file. - -```python -sess = tf.InteractiveSession() -``` - -## Computational Convenience Functions - - -```python -def make_kernel(a): - """Transform a 2D array into a convolution kernel""" - 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) -``` - -## Define the PDE - -Our pond is a perfect 500 x 500 square, as is the case for most ponds found in -nature. - -```python -N = 500 -``` - -Here we create our pond and hit it with some rain drops. - -```python -# Initial Conditions -- some rain drops hit a pond - -# Set everything to zero -u_init = np.zeros([N, N], dtype=np.float32) -ut_init = np.zeros([N, N], dtype=np.float32) - -# Some rain drops hit a pond at random points -for n in range(40): - a,b = np.random.randint(0, N, 2) - u_init[a,b] = np.random.uniform() - -DisplayArray(u_init, rng=[-0.1, 0.1]) -``` - - - - -Now let's specify the details of the differential equation. - - -```python -# Parameters: -# eps -- time resolution -# damping -- wave damping -eps = tf.placeholder(tf.float32, shape=()) -damping = tf.placeholder(tf.float32, shape=()) - -# Create variables for simulation state -U = tf.Variable(u_init) -Ut = tf.Variable(ut_init) - -# Discretized PDE update rules -U_ = U + eps * Ut -Ut_ = Ut + eps * (laplace(U) - damping * Ut) - -# Operation to update the state -step = tf.group( - U.assign(U_), - Ut.assign(Ut_)) -``` - -## Run The Simulation - -This is where it gets fun -- running time forward with a simple for loop. - -```python -# Initialize state to initial conditions -tf.global_variables_initializer().run() - -# Run 1000 steps of PDE -for i in range(1000): - # Step simulation - step.run({eps: 0.03, damping: 0.04}) - DisplayArray(U.eval(), rng=[-0.1, 0.1]) -``` - - - -Look! Ripples! |