Square Root Approximation of the Infinitesimal Generator for Molecular Systems

Molecular dynamics can be modelled as a stochastic process governed by a mathematical operator called infinitesimal generator which describes the kinetic properties of the system in terms of rates.
Square Root Approximation (SqRA) is a method to discretize the infinitesimal generator into a transition rate matrix.
Assuming a Voronoi tessellation of the state space, the rate between two adjacent cells is approximated as the product of two terms: the geometric average of the Boltzmann weights of the cells, and the flux of the configurations through the intersecting surface.
The first term is estimated from the potential energy function, while the second depends on the diffusion constant and the grid used for the discretization.
SqRA does not require to integrate the associated stochastic differential equation and it can be useful to study molecular dynamics reducing significantly the computational cost.
We present the underlaying theory of SqRA and the results that demonstrate the computational efficiency and the accuracy of the method.