Inverse Monte Carlo method

Lyubartsev has also developed a multiscale parameterisation method that has been used to systematically build a CG model of a DMPC bilayer. Lyubartsev uses an inverse Monte Carlo method to generate the CG parameters from an underlying atomistic simulation. The atomistic simulation trajectory is analysed to generate the radial distribution functions (RDFs) for the CG bead model. These RDFs can be converted into pairwise interaction potentials between the beads. The... 

M. Oguma and J. R. Howell, Solution of T vo-Dimensional Blackbody Inverse Radiation by an Inverse Monte Carlo Method, Proc. 4th ASMEIJSME Joint Symposium, Maui, March, 1995. 

IMC inverse Monte Carlo (method) gSR muon spin relaxation... 

In structure matching methods, potentials between the CG sites are determined by fitting structural properties, typically radial distribution functions (RDF), obtained from MD employing the CG potential (CG-MD), to those of the original atomistic system. This is often achieved by either of two closely related methods, Inverse Monte Carlo [12-15] and Boltzmann Inversion [5, 16-22], Both of these methods refine the CG potentials iteratively such that the RDF obtained from the CG-MD approaches the corresponding RDF from an atomistic MD simulation. 

Both the inverse Monte Carlo and iterative Boltzmann inversion methods are semi-automatic since the radial distribution function needs to be re-evaluated at... 

To illustrate the application of the Monte Carlo method, we consider the problem of simulating the dispersion of material emitted from a continuous line source located between the ground and an inversion layer. A similar case has been considered by Runca et al. (1981). We assume that the mean wind u is constant and that the slender-plume approximation holds. The line source is located at a height h between the ground (z = 0) and an inversion layer (z = Zi). If the ground is perfectly reflecting, the analytical expression for the mean concentration is found by integrating the last entry of Table II over y from -< to -Hoo. The result can be expressed as... 

RDFs calculated from a CG simulation using these initial interaction potentials differ from those calculated from the atomistic simulation. An inverse Monte Carlo algorithm is therefore used to iteratively refine these interaction potentials by correcting them by the difference between the CG and atomistic RDFs. This is essentially the same method that was used by Shelley et al to derive the parameters between the CG lipid head group particles, and is also similar to the Boltzmann inversion method, " which also uses an iterative procedure that uses RDFs measured from atomistic simulations to derive CG interaction potentials. Lyubartsev has used this method to fully parameterize his own CG model of DMPC. 

Methods for calculating these quantities are discussed in detail in the book by Holbrook, Pilling and Robertson [29]. These methods fall into several basic categories - classical approximations, inversion of the partition function, direct count methods and Monte Carlo methods, each of which is introduced briefly. 

For either the accurate or approximate computation of the high dimensional integrals occurring in many electron atomic and molecular problems, the most efficient numerical integration scheme developed hitherto is Conroy s recently reported closed Diophantine method. This procedure, an improvement over Haselgrove s open method shares the advantage with Monte Carlo methods of not suffering from the dimensional effect. Moreover, its associated error ideally decreases with the inverse square of the number of sample points, whereas that associated with Monte Carlo methods shows at most an inverse square root dependence upon this number. 

We now show that the value of x selected above is the same as would be chosen from a Monte Carlo method. The probability of finding the oscillator within dx of x is inversely proportional to x (the slower x is traversed, the more chance of finding the system near that x value). 

This search for ever-increasing efficiency has led to ingenious simulation algorithms, some of which are fairly removed from reality in that molecules are broken and reconnected, hypothetical and often unphysical thermodynamic paths are constructed, the natural fluctuations of a system are arbitrarily enhanced or suppressed, molecules are created or destroyed, etc. Indeed, half-Jokingly one could almost venture that the efficiency of a Monte Carlo method is inversely proportional to its resemblance to reality. Just as Monte Carlo methods have evolved, however, the power of computers has been steadily increasing it is conceivable that simulators will eventually return to simpler and more transparent simulation techniques that were not possible on smaller and slower machines. 

Myers et al. (2007, 2009) introduced a Bayesian nonlinear inversion framework to multiple-event analysis (Bayesloc). The nonlinear Markov chain Monte Carlo method enables Bayesloc to simultaneously assess the joint posterior distribution spanning event locations, travel-time corrections, phase names, and arrival-time measurement precision. Myers et al. (2011) demonstrated that Bayesloc can be applied to data sets of tens of thousands of events and millions of arrivals because the solution does not involve direct inversion of a matrix and computation demands grow linearly with the number of arrivals. 

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