def test_kohn_sham_neural_xc_density_mse_converge_tolerance(
self, density_mse_converge_tolerance, expected_converged):
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(8), stax.Elu, stax.Dense(1)))
params_init = init_fn(rng=random.PRNGKey(0))
states = jit_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=params_init),
interaction_fn=utils.exponential_coulomb,
initial_density=self.num_electrons *
utils.gaussian(grids=self.grids, center=0., sigma=0.5),
density_mse_converge_tolerance=density_mse_converge_tolerance)
np.testing.assert_array_equal(states.converged, expected_converged)
for single_state in scf.state_iterator(states):
self._test_state(
single_state,
self._create_testing_external_potential(
utils.exponential_coulomb))
def test_local_density_approximation_wrong_output_shape(self):
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(16), stax.Elu, stax.Dense(3)))
init_params = init_fn(rng=random.PRNGKey(0))
with self.assertRaisesRegex(
ValueError, r'The output shape of the network '
r'should be \(-1, 1\) but got \(11, 3\)'):
xc_energy_density_fn(self.density, init_params)
def test_local_density_approximation(self):
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(16), stax.Elu, stax.Dense(1)))
init_params = init_fn(rng=random.PRNGKey(0))
xc_energy_density = xc_energy_density_fn(self.density, init_params)
# The first layer of the network takes 1 feature (density).
self.assertEqual(init_params[0][0].shape, (1, 16))
self.assertEqual(xc_energy_density.shape, (11, ))
def test_kohn_sham_iteration_neural_xc(self, interaction_fn,
enforce_reflection_symmetry):
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(8), stax.Elu, stax.Dense(1)))
params_init = init_fn(rng=random.PRNGKey(0))
initial_state = self._create_testing_initial_state(interaction_fn)
next_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=params_init),
interaction_fn=interaction_fn,
enforce_reflection_symmetry=enforce_reflection_symmetry)
self._test_state(next_state, initial_state)
def test_kohn_sham_neural_xc(self, interaction_fn):
init_fn, xc_energy_density_fn = neural_xc.local_density_approximation(
stax.serial(stax.Dense(8), stax.Elu, stax.Dense(1)))
params_init = init_fn(rng=random.PRNGKey(0))
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=params_init),
interaction_fn=interaction_fn)
for single_state in scf.state_iterator(state):
self._test_state(
single_state,
self._create_testing_external_potential(interaction_fn))
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, [0.2013181, 0.], atol=1e-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=1e-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, [-1.40994668, -2.58881225])
# 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=3e-4)
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)