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POEM ID: 019
Title: Random Vectors in Directional Derivatives
authors: [kejacobson] (Kevin Jacobson)
Competing POEMs: [N/A]
Related POEMs: [N/A]
Associated implementation PR:

Status:

  • Active
  • Requesting decision
  • Accepted
  • Rejected
  • Integrated

Motivation

This POEM is a request for an additional option for partial derivative checking with directional derivatives. The motivating use case is partial checking of high-fidelity analysis components that may have large input and output vectors. For those types of components, directional derivatives are essential The current vector in the implementation of directional derivatives is a uniform vector of ones, [1,1,1,1,...], but this is inadequate for testing some types of components. For example, a computational fluid dynamics component where the input is the vector of mesh coordinates. If you apply a uniform perturbation to the mesh coordinates, the mesh translates, but the flow state, lift, drag, etc. will not change. But, a random perturbation vector can properly exercise the component. Another example is a component that fits a rotation to a set of displaced points. With the uniform vector, the rotation is zero and the directional derivative is zero.

Description

Although it may be possible change the expected type of directional from boolean to string, it may be better for backwards compatibility to add a new optional argument to set_check_partial_options to control the type of vector.

def setup(self):
    self.set_check_partial_options(wrt='*',directional=True,direction='random')

The options for direction could be 'uniform', 'random', or 'seeded_random'. 'uniform' is the current approach. The 'seeded_random', potentially seeding on the vector size or some other consistent value, can useful for getting a consistent answer for debugging partials without a uniform vector. The 'random' option gives a different perturbation vector each time which is also useful. Running check partials multiple times with a new random vectors gives more confidence in the result.

The pseudocode looks something like:


if 'random' in direction:
  if 'seeded' in direction:
    np.random.seed(seed_value)
  self.perturb_vec =  np.random.random_sample(input.shape) - 0.5 # offset to get both positive and negative perturbations
else:
  self.perturb_vec = np.ones(input.shape)

# setting up the finite difference inputs, where delta is the real or complex step size
input_perturbed[:] = input[:] + delta * self.perturb_vec
.
.
.
# setting up the forward mode partial
d_input = self.perturb_vec

This method feeds into the dot product test for adjoints where perturb_vec is m. With a second perturbation vector of the size of the outputs, d, the forward and reverse mode partials can be checked with one call for the forward mode and one for the reverse mode.