.. _svm:

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Support Vector Machine Applications
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Optimizing Transition State Theory Dividing Surfaces
======================================================

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.
[#Pozun12_174101]_

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]}

			**kernel** : specifies the kernel used ('rbf'(radial basis function),'linear','polynomial'
					'sigmoid')

			**gamma** : the most commonly used kernel is rbf; this parameter determines the gaussian
				    radius and the values used in cross validation  

			**C** : range 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 [#Pozun12_174101]_. 

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 


Accelerated Molecular Dynamics with Support Vector Machines
============================================================

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 [#Xiao15_244104]_. 


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

.. rubric:: References
.. [#Pozun12_174101] Z. D. 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 <http://dx.doi.org/10.1063/1.4707167>`_

.. [#Xiao15_244104] P. Xiao, J. Duncan, L. Zhang, and G. Henkelman, Ridge-Based Bias Potentials to Accelerate Molecular Dynamics, J. Chem. Phys. 143, H3061 (2015)