Data assimilation using a GPU accelerated path integral Monte Carlo approach

The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a graphics processing unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin–Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.     

Monte Carlo integration for lattice gauge theories with fermions

A Monte Carlo procedure is constructed for lattice gauge theories with fermions by replacing integration over fermion degrees of freedom in the path integral by conventional integration over effective boson degrees of freedom. The method is applied to gauge theories over two discrete subgroups of SU(2).     

Geometrical form factor calculation using Monte Carlo integration for lidar

We proposed a geometrical form factor (GFF) calculation using Monte Carlo integration (GFF–MC) for lidar that is practical and can be applied to any laser intensity distribution. Theoretical results have been calculated with our method based on the functions of measured, uniform and Gaussian laser intensity distribution. Two experimental GFF traces on clear days are obtained to verify the validity of the theoretical results. The results indicated that the measured distribution function outperformed the Gaussian and uniform functions. That means that the deviation of the measured laser intensity distribution from an ideal one can be too large to neglect. In addition, the theoretical GFF of the uniform distribution had a larger error than that of the Gaussian distribution. Furthermore, the effects of the inclination angle of the laser beam and the central obstruction of the support structure of the second mirror of the telescope are discussed in this study.     

GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.     

Monte Carlo Hamiltonian

We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.     

Momentum-space Monte Carlo

Using the quenched, reduced form of large-N field theories, we show that it is possible to directly measure momentum-space Green functions, via Monte Carlo, without going through the intermediate step of measurement in position space plus Fourier transformation. This promises to be useful tool for investigating the infrared structure of planar field theories. As an application (and test) of the method, we compute mass-gaps in the quenched U(N) × U(N) lattice chiral model, in D = 1 and 2 dimensions.     

LED梯度折射率封装结构的蒙特卡罗模拟

针对封装胶中掺杂纳米颗粒以及采用梯度折射率的LED封装模式,用蒙特卡罗方法模拟光在胶体中的传播,分析散射系数对透光率的影响.结果表明,透光率随散射系数增大而减小.对于固定的封装层数,各层均采取最佳折射率值时,透光率可以达到最大.梯度折射率值逐渐减小的多层纳米掺杂封装结构,透光率高于传统的封装模式,能够提高LED的出光效率.     

LED梯度折射率封装结构的蒙特卡罗模拟

针对封装胶中掺杂纳米颗粒以及采用梯度折射率的LED封装模式,用蒙特卡罗方法模拟光在胶体中的传播,分析散射系数对透光率的影响.结果表明,透光率随散射系数增大而减小.对于固定的封装层数,各层均采取最佳折射率值时,透光率可以达到最大.梯度折射率值逐渐减小的多层纳米掺杂封装结构,透光率高于传统的封装模式,能够提高LED的出光效率.     

Fractional volume integration in two-dimensional NMR spectra: CAKE, a Monte Carlo approach

Quantitative information from multi-dimensional NMR experiments can be obtained by peak volume integration. The standard procedure (selection of a region around the chosen peak and addition of all values) is often biased by poor peak definition because of peak overlap. Here we describe a simple method, called CAKE, for volume integration of (partially) overlapping peaks. Assuming the axial symmetry of two-dimensional NMR peaks, as it occurs in NOESY and TOCSY when Lorentz-Gauss transformation of the signals is carried out, CAKE estimates the peak volume by multiplying a volume fraction by a factor R. It represents a proportionality ratio between the total and the fractional volume, which is identified as a slice in an exposed region of the overlapping peaks. The volume fraction is obtained via Monte Carlo Hit-or-Miss technique, which proved to be the most efficient because of the small region and the limited number of points within the selected area. Tests on simulated and experimental peaks, with different degrees of overlap and signal-to-noise ratios, show that CAKE results in improved volume estimates. A main advantage of CAKE is that the volume fraction can be flexibly chosen so as to minimize the effect of overlap, frequently observed in two-dimensional spectra.     

系综Monte Carlo方法

本文系统地给出了Monte Carlo模拟的一般方法在各种系综条件下的表述以及它们的算法。     

Virial-bias Monte Carlo methods

A new sampling technique is proposed for the isothermal-isobaric (T, P, N) ensemble Monte Carlo computer simulation. The new method selects the volume perturbations by using the partial derivative of the volume with respect to the internal energy. Test calculations on the Lennard-Jones fluid show significant improvements over the conventionally used method.     

Monte Carlo renormalization group

Monte Carlo computer simulations have long been used to obtain information on the behavior of thermodynamic systems. The method has the advantages of being applicable to a very large class of models and of using only systematically improvable approximations (finite size of system, statistical errors, etc.). However, in the critical region, finite-size effects mask the critical singularities, and put severe practical limits onto the accuracy to which the true critical behavior can be determined. By combining Monte Carlo simulations with a real-space renormalization-group analysis, a large increase in efficiency and accuracy can be achieved—without the uncertainties of the usual truncation approximations. The methods are illustrated by explicit calculations on models exhibiting critical and tricritical behavior.     

Broad histogram Monte Carlo

We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass. Received: 8 August 1997 / Revised: 11 August 1997 / Accepted: 30 October 1997     

Auxiliary-field Monte Carlo methods

I discuss Monte Carlo algorithms for quantum many-body systems that employ an auxiliary field to linearize a two-body interaction. These reduce the evaluation of the partition function to sampling many one-body evolutions in a fluctuating field. Fermions and bosons are treated on an equal footing. Applications to potential models and to quantum spin systems are discussed. This work was supported in part by the National Science Foundation, grants PHY82-07332 and PHY85-05682. The potential-model studies were done in collaboration with G. Sugiyama, while A. Khan and T. Troudet were responsible for the work on the quantum spin systems.     

Diffusion Monte Carlo calculations on LaB molecule

Potential energy curves for the lowest electronic states of LaB and LaB~- have been calculated by ab initio calculations.The diffusion Monte Carlo method has been employed in combination with three different trial functions. Spectroscopic constants have also been numerically derived for the neutral molecule and compared with the only available theoretical work;~([19]) however, predictions are provided for the corresponding constants for the anionic species which have not been reported yet. Our calculations suggest the high spin quintet state of LaB as the ground state with the triplet state higher in energy irrespective of the type of the functional used. This suggestion is in good accordance with the previous theoretical results calculated at B3LYP/LANL2DZ level of theory, whereas it contradicts with the prediction based upon B3LYP/SDD calculations in the same study. Moreover, variations of the permanent dipole moments as a function of the internuclear separations for the two electronic states of the neutral molecule have been studied and analyzed.