A method for optimizing Transition State Theory (TST) divding surfaces was developed using two-class support vector machines (SVM) that does not require prior knowledge of the system. The TST dividing surface is optimized by a cycle of machine learning and refinement by using molecular dynamics (MD). More implementation details with citation. 1
The function below takes a labeled training set of two classes (e.g. reactant and products) and applies the two class support vecort machine algorithm. Parameters are selected using cross validation, which requires a test training set.
def tsase.svm. learn_svm (parameters, datapoints, datalabels, datapointstest, datalabelstest, kval=2):
parameters : a list of parameters to use for two class svm; below is an exaple:
parameters = {‘kernel’:[‘rbf’], ‘gamma’:[1e0,5e0,1e1,5e1,1e2], ‘C’:[1e2,1e3,1e4,1e5]}
- kernelspecifies the kernel used (‘rbf’(radial basis function),’linear’,’polynomial’
‘sigmoid’)
- gammathe most commonly used kernel is rbf; this parameter determines the gaussian
radius and the values used in cross validation
- Crange of values of used in cross validation for parameter C; this parameter
determines the trade off between a misclassification of points maximizing the margin between classes
datapoints : training set
datalabels : labels corresponding to training set
datapointstest : test training set
datalabelstest : labels corresponding to test training set
kval : parameter for k-cross validation; determines the number of partitions of training set
This function sets up a potential to run dynamics for refining the TST dividing surface as oulined in 1.
class tsase.svm. svm_dynamics ( calc, selSVM, k=1.0, addgradient=True)
calc : atoms object
selSVM : two class SVM hypersurface generated from the learn_svm function
k : spring constant for MD sampling close to SVM hypersurface
addgradient : option to add the gradient for the biased sampling
Hyperdynamics is a method for accelerating molecular dynamic simulations, where a positive bias potential that goes to zero at the TST divding surface is added to the potential energy landscape to lower barriers between states. A method was developed using one-class support vector machine (OCSVM) to generate a bias potential for the hyperdynamics. By running high temperature MD constrained to a reactant state, OCSVM can find a hypersurface enclosing the region where the system is most probable. A bias potential is constructed by finding the closest distance to this hypersurface. More implementation of details with citation 2.
Given a training set obtained from high temperature MD the following function can be used to find the OCSVM hypersurface:
def tsase.svm. learn_ocsvm (datapoints,gam,nu):
datapoints : OCSVM training set
gam : This function uses the radial basis function kernal. This parameter defines the gaussian radius.
nu : This parameter defines a lower bound on the fraction of support vectors and an upper bound on the fraction of outliers
The following class runs molecular dynamics on the biased potential energy surface given a ocsvm hypersurface obtained from the function above.
class tsase.svm. ocsvm_dynamics ( p, clf, csda_cc=0.001, cdsa_maxstep=1.0, w=1.0, B=1.0, fixcm=False,dt=1.0, kT=0.1)
p : atoms object
clf : ocsvm hypersurface obtained from the learn_ocsvm function
cdsa_cc : the closest distance to the surface algorithm (cdsa) convergence criteria
cdsa_maxstep : a maximum allowed step for the cdsa
w : parameter which determines the distance in which the bias potential switches between a constant form and a polynomial.
B : parameter which determines the maximum boost
fixcm : If True, the position and momentum of the center of mass is kept constant
dt : timestep
kT : temperature in kT; this is need to calculate appropriate boost factor and renormalization of the time
References
Pozun, K. Hansen, D. Sheppard, M. Rupp, K.-R. Müller, and G. Henkelman, Optimizing transition states via kernel-based machine learning, J. Chem. Phys. 136, 174101 DOI
Xiao, J. Duncan, L. Zhang, and G. Henkelman, Ridge-Based Bias Potentials to Accelerate Molecular Dynamics, J. Chem. Phys. 143, H3061 (2015)