Paper Info
Title
Multidimensional integration through Markovian sampling under steered function morphing: A physical guise from statistical mechanics.
Abstract
We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial appropriate profile. Thanks to an abstract reformulation of Jarzynski’s equality applied in stochastic thermodynamics to evaluate the free-energy profiles along selected reaction coordinates via non-equilibrium transformations, it is possible to cast the original integral into the exponential average of the distribution of the pseudo-work (that we may term “computational work”) involved in doing the function morphing, which is straightforwardly solved. Several tests illustrate the basic implementation of the idea, and show its performance in terms of computational time, accuracy and precision. The formulation for integrand functions with zeros and possible sign changes is also presented.
Year
DOI
Venue
2015
10.1016/j.cpc.2015.04.010
Computer Physics Communications
Keywords
Field
DocType
Multidimensional integration,Stochastic sampling,Jarzynski equality
Byte,Morphing,Mathematical optimization,Markov process,Exponential function,Identifier,Mathematical analysis,Unix,Test data,Mathematics,Jarzynski equality
Journal
Volume
ISSN
Citations 
195
0010-4655
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Mirco Zerbetto131.88
Diego Frezzato231.19