import numpy as np
import pickle
import warnings
from scipy.optimize import minimize
from ase.parallel import world
from ase.optimize.optimize import Optimizer
from ase.optimize.gpmin.gp import GaussianProcess
from ase.optimize.gpmin.kernel import SquaredExponential
from ase.optimize.gpmin.prior import ConstantPrior
[docs]class GPMin(Optimizer, GaussianProcess):
def __init__(self, atoms, restart=None, logfile='-', trajectory=None,
prior=None, kernel=None, master=None, noise=None, weight=None,
scale=None, force_consistent=None, batch_size=None,
bounds=None, update_prior_strategy="maximum",
update_hyperparams=False):
"""Optimize atomic positions using GPMin algorithm, which uses both
potential energies and forces information to build a PES via Gaussian
Process (GP) regression and then minimizes it.
Default behaviour:
--------------------
The default values of the scale, noise, weight, batch_size and bounds
parameters depend on the value of update_hyperparams. In order to get
the default value of any of them, they should be set up to None.
Default values are:
update_hyperparams = True
scale : 0.3
noise : 0.004
weight: 2.
bounds: 0.1
batch_size: 1
update_hyperparams = False
scale : 0.4
noise : 0.005
weight: 1.
bounds: irrelevant
batch_size: irrelevant
Parameters:
------------------
atoms: Atoms object
The Atoms object to relax.
restart: string
Pickle file used to store the training set. If set, file with
such a name will be searched and the data in the file incorporated
to the new training set, if the file exists.
logfile: file object or str
If *logfile* is a string, a file with that name will be opened.
Use '-' for stdout
trajectory: string
Pickle file used to store trajectory of atomic movement.
master: boolean
Defaults to None, which causes only rank 0 to save files. If
set to True, this rank will save files.
force_consistent: boolean or None
Use force-consistent energy calls (as opposed to the energy
extrapolated to 0 K). By default (force_consistent=None) uses
force-consistent energies if available in the calculator, but
falls back to force_consistent=False if not.
prior: Prior object or None
Prior for the GP regression of the PES surface
See ase.optimize.gpmin.prior
If *prior* is None, then it is set as the
ConstantPrior with the constant being updated
using the update_prior_strategy specified as a parameter
kernel: Kernel object or None
Kernel for the GP regression of the PES surface
See ase.optimize.gpmin.kernel
If *kernel* is None the SquaredExponential kernel is used.
Note: It needs to be a kernel with derivatives!!!!!
noise: float
Regularization parameter for the Gaussian Process Regression.
weight: float
Prefactor of the Squared Exponential kernel.
If *update_hyperparams* is False, changing this parameter
has no effect on the dynamics of the algorithm.
update_prior_strategy: string
Strategy to update the constant from the ConstantPrior
when more data is collected. It does only work when
Prior = None
options:
'maximum': update the prior to the maximum sampled energy
'init' : fix the prior to the initial energy
'average': use the average of sampled energies as prior
scale: float
scale of the Squared Exponential Kernel
update_hyperparams: boolean
Update the scale of the Squared exponential kernel
every batch_size-th iteration by maximizing the
marginal likelihood.
batch_size: int
Number of new points in the sample before updating
the hyperparameters.
Only relevant if the optimizer is executed in update_hyperparams
mode: (update_hyperparams = True)
bounds: float, 0<bounds<1
Set bounds to the optimization of the hyperparameters.
Let t be a hyperparameter. Then it is optimized under the
constraint (1-bound)*t_0 <= t <= (1+bound)*t_0
where t_0 is the value of the hyperparameter in the previous
step.
If bounds is False, no constraints are set in the optimization of
the hyperparameters.
.. warning:: The memory of the optimizer scales as O(n²N²) where
N is the number of atoms and n the number of steps.
If the number of atoms is sufficiently high, this
may cause a memory issue.
This class prints a warning if the user tries to
run GPMin with more than 100 atoms in the unit cell.
"""
# Warn the user if the number of atoms is very large
if len(atoms) > 100:
warning = ('Possible Memory Issue. There are more than '
'100 atoms in the unit cell. The memory '
'of the process will increase with the number '
'of steps, potentially causing a memory issue. '
'Consider using a different optimizer.')
warnings.warn(warning)
# Give it default hyperparameters
if update_hyperparams: # Updated GPMin
if scale is None:
scale = 0.3
if noise is None:
noise = 0.004
if weight is None:
weight = 2.
if bounds is None:
self.eps = 0.1
elif bounds is False:
self.eps = None
else:
self.eps = bounds
if batch_size is None:
self.nbatch = 1
else:
self.nbatch = batch_size
else: # GPMin without updates
if scale is None:
scale = 0.4
if noise is None:
noise = 0.001
if weight is None:
weight = 1.
if bounds is not None:
warning = ('The parameter bounds is of no use '
'if update_hyperparams is False. '
'The value provided by the user '
'is being ignored.')
warnings.warn(warning, UserWarning)
if batch_size is not None:
warning = ('The parameter batch_size is of no use '
'if update_hyperparams is False. '
'The value provided by the user '
'is being ignored.')
warnings.warn(warning, UserWarning)
# Set the variables to something anyways
self.eps = False
self.nbatch = None
self.strategy = update_prior_strategy
self.update_hp = update_hyperparams
self.function_calls = 1
self.force_calls = 0
self.x_list = [] # Training set features
self.y_list = [] # Training set targets
Optimizer.__init__(self, atoms, restart, logfile,
trajectory, master, force_consistent)
if prior is None:
self.update_prior = True
prior = ConstantPrior(constant=None)
else:
self.update_prior = False
if kernel is None:
kernel = SquaredExponential()
GaussianProcess.__init__(self, prior, kernel)
self.set_hyperparams(np.array([weight, scale, noise]))
def acquisition(self, r):
e = self.predict(r)
return e[0], e[1:]
def update(self, r, e, f):
"""Update the PES
Update the training set, the prior and the hyperparameters.
Finally, train the model
"""
# update the training set
self.x_list.append(r)
f = f.reshape(-1)
y = np.append(np.array(e).reshape(-1), -f)
self.y_list.append(y)
# Set/update the constant for the prior
if self.update_prior:
if self.strategy == 'average':
av_e = np.mean(np.array(self.y_list)[:, 0])
self.prior.set_constant(av_e)
elif self.strategy == 'maximum':
max_e = np.max(np.array(self.y_list)[:, 0])
self.prior.set_constant(max_e)
elif self.strategy == 'init':
self.prior.set_constant(e)
self.update_prior = False
# update hyperparams
if (self.update_hp and self.function_calls % self.nbatch == 0 and
self.function_calls != 0):
self.fit_to_batch()
# build the model
self.train(np.array(self.x_list), np.array(self.y_list))
def relax_model(self, r0):
result = minimize(self.acquisition, r0, method='L-BFGS-B', jac=True)
if result.success:
return result.x
else:
self.dump()
raise RuntimeError("The minimization of the acquisition function "
"has not converged")
def fit_to_batch(self):
"""Fit hyperparameters keeping the ratio noise/weight fixed"""
ratio = self.noise/self.kernel.weight
self.fit_hyperparameters(np.array(self.x_list),
np.array(self.y_list), eps=self.eps)
self.noise = ratio*self.kernel.weight
def step(self, f=None):
atoms = self.atoms
if f is None:
f = atoms.get_forces()
fc = self.force_consistent
r0 = atoms.get_positions().reshape(-1)
e0 = atoms.get_potential_energy(force_consistent=fc)
self.update(r0, e0, f)
r1 = self.relax_model(r0)
self.atoms.set_positions(r1.reshape(-1, 3))
e1 = self.atoms.get_potential_energy(force_consistent=fc)
f1 = self.atoms.get_forces()
self.function_calls += 1
self.force_calls += 1
count = 0
while e1 >= e0:
self.update(r1, e1, f1)
r1 = self.relax_model(r0)
self.atoms.set_positions(r1.reshape(-1, 3))
e1 = self.atoms.get_potential_energy(force_consistent=fc)
f1 = self.atoms.get_forces()
self.function_calls += 1
self.force_calls += 1
if self.converged(f1):
break
count += 1
if count == 30:
raise RuntimeError("A descent model could not be built")
self.dump()
def dump(self):
"""Save the training set"""
if world.rank == 0 and self.restart is not None:
with open(self.restart, 'wb') as fd:
pickle.dump((self.x_list, self.y_list), fd, protocol=2)
def read(self):
self.x_list, self.y_list = self.load()