def test_flatten(self):
(tree, shapes), vec = np_utils.flatten([(jnp.array([1, 2, 3]),
(jnp.array([4, 5]))),
jnp.array([99])])
self.assertIsInstance(vec, np.ndarray)
np.testing.assert_allclose(vec, [1., 2., 3., 4., 5., 99.])
self.assertEqual(shapes, [(3, ), (2, ), (1, )])
# unflatten should convert 1d array back to pytree.
params = np_utils.unflatten((tree, shapes), vec)
self.assertIsInstance(params[0][0], np.ndarray)
np.testing.assert_allclose(params[0][0], [1., 2., 3.])
self.assertIsInstance(params[0][1], np.ndarray)
np.testing.assert_allclose(params[0][1], [4., 5.])
self.assertIsInstance(params[1], np.ndarray)
np.testing.assert_allclose(params[1], [99.])
def test_kohn_sham_iteration_neural_xc_density_loss_gradient_symmetry(self):
# The network only has one layer.
# The initial params contains weights with shape (1, 1) and bias (1,).
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(1)))
init_params = init_fn(rng=random.PRNGKey(0))
initial_state = self._create_testing_initial_state(
utils.exponential_coulomb)
target_density = (
utils.gaussian(grids=self.grids, center=-0.5, sigma=1.)
+ utils.gaussian(grids=self.grids, center=0.5, sigma=1.))
spec, flatten_init_params = np_utils.flatten(init_params)
def loss(flatten_params, initial_state, target_density):
state = scf.kohn_sham_iteration(
state=initial_state,
num_electrons=self.num_electrons,
xc_energy_density_fn=tree_util.Partial(
xc_energy_density_fn,
params=np_utils.unflatten(spec, flatten_params)),
interaction_fn=utils.exponential_coulomb,
enforce_reflection_symmetry=True)
return jnp.sum(jnp.abs(state.density - target_density)) * utils.get_dx(
self.grids)
grad_fn = jax.grad(loss)
params_grad = grad_fn(
flatten_init_params,
initial_state=initial_state,
target_density=target_density)
# Check gradient values.
np.testing.assert_allclose(params_grad, [-1.34137017, 0.], atol=5e-7)
# Check whether the gradient values match the numerical gradient.
np.testing.assert_allclose(
optimize.approx_fprime(
xk=flatten_init_params,
f=functools.partial(
loss,
initial_state=initial_state,
target_density=target_density),
epsilon=1e-9),
params_grad, atol=2e-4)
def test_kohn_sham_iteration_neural_xc_energy_loss_gradient(self):
# The network only has one layer.
# The initial params contains weights with shape (1, 1) and bias (1,).
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(1)))
init_params = init_fn(rng=random.PRNGKey(0))
initial_state = self._create_testing_initial_state(
utils.exponential_coulomb)
target_energy = 2.
spec, flatten_init_params = np_utils.flatten(init_params)
def loss(flatten_params, initial_state, target_energy):
state = scf.kohn_sham_iteration(
state=initial_state,
num_electrons=self.num_electrons,
xc_energy_density_fn=tree_util.Partial(
xc_energy_density_fn,
params=np_utils.unflatten(spec, flatten_params)),
interaction_fn=utils.exponential_coulomb,
enforce_reflection_symmetry=True)
return (state.total_energy - target_energy) ** 2
grad_fn = jax.grad(loss)
params_grad = grad_fn(
flatten_init_params,
initial_state=initial_state,
target_energy=target_energy)
# Check gradient values.
np.testing.assert_allclose(params_grad, [-8.549952, -14.754195])
# Check whether the gradient values match the numerical gradient.
np.testing.assert_allclose(
optimize.approx_fprime(
xk=flatten_init_params,
f=functools.partial(
loss, initial_state=initial_state, target_energy=target_energy),
epsilon=1e-9),
params_grad, atol=2e-3)
def test_kohn_sham_neural_xc_energy_loss_gradient(self):
# The network only has one layer.
# The initial params contains weights with shape (1, 1) and bias (1,).
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(1)))
init_params = init_fn(rng=random.PRNGKey(0))
target_energy = 2.
spec, flatten_init_params = np_utils.flatten(init_params)
def loss(flatten_params, target_energy):
state = scf.kohn_sham(
locations=self.locations,
nuclear_charges=self.nuclear_charges,
num_electrons=self.num_electrons,
num_iterations=3,
grids=self.grids,
xc_energy_density_fn=tree_util.Partial(
xc_energy_density_fn,
params=np_utils.unflatten(spec, flatten_params)),
interaction_fn=utils.exponential_coulomb)
final_state = scf.get_final_state(state)
return (final_state.total_energy - target_energy) ** 2
grad_fn = jax.grad(loss)
params_grad = grad_fn(flatten_init_params, target_energy=target_energy)
# Check gradient values.
np.testing.assert_allclose(params_grad, [-3.908153, -5.448675], atol=1e-6)
# Check whether the gradient values match the numerical gradient.
np.testing.assert_allclose(
optimize.approx_fprime(
xk=flatten_init_params,
f=functools.partial(loss, target_energy=target_energy),
epsilon=1e-8),
params_grad, atol=5e-3)
