TensorFlow: integrate output of neural network

Question

I have a neural network that takes as input two parameters:

t = tf.placeholder(tf.float32, [None, 1])
x = tf.placeholder(tf.float32, [None, 1])

in my loss function I need to integrate the output over t, but I can't figure out a way of doing this, because the only numerical integration function available in TensorFlow, tf.contrib.integrate.odeint_fixed, cannot take a Tensor as function, since it can't be called:

Call

t = tf.constant(np.linspace(0.0,1.0,100), dtype = tf.float64 )

integ = tf.contrib.integrate.odeint_fixed(model.output, 
                                          0.0, 
                                          t, 
                                          method = "rk4")

Output

...

<ipython-input-5-c79e79b75391> in loss(model, t, x)
     24                                                 0.0,
     25                                                 t,
---> 26                                                 method = "rk4")

...

TypeError: 'Tensor' object is not callable

Not to mention that I'm also clueless on how to treat x in this computation, it's supposed to be held fixed.

Answer 1

tf.contrib.integrate.odeint_fixed appears to be for integrating ordinary differential equations (ODEs). If I understand you correctly, however, you want to approximate the definite integral of your model's output, let's call it y, sampled at t.

To do so, you could use the trapezoidal rule, for which you find a possible implementation in tensorflows AUC function. In your case, it could look like:

from tensorflow.python.ops import math_ops

def trapezoidal_integral_approx(t, y):
    return math_ops.reduce_sum(
            math_ops.multiply(t[:-1] - t[1:],
                              (y[:-1] + y[1:]) / 2.), 
            name='trapezoidal_integral_approx')

where y would be the output of your model.