def processGradients(self, grads, fields):
processedGrads = grads
processedGrads[0] = grads[0] / (2 * np.pi * tf.cast(
tf.reshape(self.metric, tf.concat([self.latShape, [1, 1]], 0)),
tf.complex128))
processedGrads[1] = FieldTools.projectSu2Gradients(grads[1], fields[1])
processedGrads[1] = processedGrads[1] / (2 * np.pi * tf.cast(
tf.reshape(self.metric, tf.concat([self.latShape, [1, 1, 1]], 0)),
tf.complex128))
return processedGrads
minSteps = 1000 # Gets stuck in an unwanted saddle point without these
printIncrement = 10
while numSteps < minSteps or (rmsGrad > tol and numSteps < maxNumSteps):
# Compute the field energy, with tf watching the variables
with tf.GradientTape() as tape:
energy = lossFn()
vars = [scalarFieldVar, gaugeFieldVar]
# Compute the gradients using automatic differentiation
grads = tape.gradient(energy, vars)
# Postprocess the gauge field gradients so they point in the tangent space
# to SU(2)
grads[1] = FieldTools.projectSu2Gradients(grads[1], gaugeFieldVar)
# Compute max gradient for stopping criterion
gradSq = FieldTools.innerProduct(grads[0], grads[0], tr=True)
gradSq += FieldTools.innerProduct(grads[1], grads[1], tr=True, adj=True)
rmsGrad = tf.sqrt(gradSq)
if (numSteps % printIncrement == 0):
print("Energy after " + str(numSteps) + " iterations: " +\
str(energy.numpy()))
print("RSS gradient after " + str(numSteps) + " iterations: " +\
str(rmsGrad.numpy()))
# Perform the gradient descent step
opt.apply_gradients(zip(grads, vars))
def processGradients(self, grads, fields):
processedGrads = grads
processedGrads[1] = FieldTools.projectSu2Gradients(grads[1], fields[1])
return processedGrads