Nonlinear time series forecasting with Bayesian neural networks

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.     

基于Monte Carlo随机模拟的综合交通网络布局评价与决策方法

针对综合交通网络评价指标权重及属性值具有主观性和随机性的特点,提出了基于模拟运算的布局规划方案排序选优的群体随机决策方法.仿真生成满足集结的多个专家对指标重要性偏好排序统计分布的权重,同时考虑交通需求的不确定性对指标值的影响,结合客观熵权计算方案的综合评价值,由多次模拟得到的排序优势度确定方案的优劣差异.根据设计的仿真流程通过算例说明了方法应用的有效性,评价中考虑了主客观因素及随机性特征,可以为网络布局提供科学决策依据.     

SIMULATION AND ESTIMATION OF LONG MEMORY CONTINUOUS TIME MODELS

Abstract. Some general properties of long memory continuous time processes are recalled or proved. Methods of simulation are studied. A comparison with the usual discrete time autoregressive fractionally integrated moving-average filter is made and illustrations are provided. Then, two methods of estimation of the parameters of such a model from a discrete sample are studied, both theoretically and empirically, with Monte Carlo experiments.     

Unsteady radiative heat transfer within a suspension of ZnO particles undergoing thermal dissociation

An emitting, absorbing, and anisotropically scattering plain medium containing a suspension of ZnO particles is considered, in which the particles are directly exposed to high-flux irradiation and undergo shrinkage during their endothermic dissociation into Zn(g) and O₂ at above 2100 K. The unsteady energy equation that links the rate of radiative heat transfer to the rate of the chemical reaction is formulated and solved numerically by the finite volume technique and the explicit Euler time-integration scheme. The path-length Monte Carlo method is applied for modeling the radiative transfer within the suspension using the absorption/scattering coefficients and the scattering phase function obtained from the Mie theory. It is found that the particle suspension can be heated rapidly from its initial 300 K to over 1800 K in less than 0.1 s, resulting in a more uniform temperature profile as the reaction progresses, particles shrink, and the suspension becomes optically thinner. The chemical conversion increases with decreasing initial particle diameter and volume fraction due to the efficient radiative absorption.     

Radial density distribution of fractal clusters

The radial density distributions of fractal clusters generated in both DLCA and RLCA conditions by Monte-Carlo off-lattice cluster-cluster aggregation have been investigated. It has been computed by averaging a large number of clusters of same mass to form an average cluster, which is then considered as spherically symmetric. It is found that the radial density distribution, calculated using the mass center of the cluster as the center point, does not follow the fractal scaling, as sometimes assumed in the literature. An empirical model has been proposed to describe the dependence of the radial density distribution on the number of particles in the cluster. The obtained radial density distribution is used to compute permeability profile of the fractal cluster using several literature models, which is then applied to estimate the cluster hydrodynamic radius, R_h, by considering the cluster as a porous permeable object and using the solution of Brinkman equations for the fluid flow inside the cluster. The so obtained R_h values are compared to those in the literature, computed using the Kirkwood-Riseman (KR) theory. It has been found that, among the five permeability models examined, only the model proposed by Davis (Proceedings of the Institution of Mechanical Engineers Part B 1, 185) provides results in good agreement with those obtained using the KR model. Furthermore, it has been verified that the R_h values are insensitive to the model used for the density distribution.     

Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems

Monte Carlo (MC) constitutes an important class of methods for the numerical solution of the general dynamic equation (GDE) in particulate systems. We compare four such methods in a series of seven test cases that cover typical particulate mechanisms. The four MC methods studied are: time-driven direct simulation Monte Carlo (DSMC), stepwise constant-volume Monte Carlo, constant number Monte Carlo, and multi-Monte Carlo (MMC) method. These MC's are introduced briefly and applied numerically to simulate pure coagulation, breakage, condensation/evaporation (surface growth/dissolution), nucleation, and settling (deposition). We find that when run with comparable number of particles, all methods compute the size distribution within comparable levels of error. Because each method uses different approaches for advancing time, a wider margin of error is observed in the time evolution of the number and mass concentration, with event-driven methods generally providing better accuracy than time-driven methods. The computational cost depends on algorithmic details but generally, event-driven methods perform faster than time-driven methods. Overall, very good accuracy can be achieved using reasonably small numbers of simulation particles, O(10³), requiring computational times of the order 10²−10³ s on a typical desktop computer.     

Partitioning of polymers into pores with surface interactions at dilute solution limit

The partitioning of a single polymer chain into a slit in a good solvent with different surface interactions is examined through Monte Carlo simulations from subcritical regime to adsorptive regime. The chain conformation in the subcritical regime is not perturbed by the surface interactions significantly. In the adsorptive regime, the conformation of the chain is strongly perturbed by the surface interactions. The confinement free energy in the two regimes maybe written in a uniform formula, βΔμ_conf∼c₁N(a/D)^xε_w+c₂N(a/D)^1/ν with x∼2.0 or larger in the subcritical regime and ∼1.0 in the adsorptive regime, where ν is the Flory exponent, D is the slit width, N is the chain length, a is the monomer size, and ε_w is the surface interaction energy between the polymer beads and the slit. This formula is valid for a long chain in the narrow slit in the subcritical regime or when the adsorption layer h>D in the adsorptive regime. A critical behavior occurs when ε_w is at the critical adsorption point and x=1/ν, then Δμ_conf will have little dependence on N or D. Higher order terms that are neglected in the above equation, however, may be present that could lead to a weak dependence of K on N and D even in the critical adsorption point.     

TESTS FOR FRACTIONAL INTEGRATION:A MONTE CARLO INVESTIGATION

Abstract. The performance of the Geweke-Porter-Hudak (GPH) test, the modified rescaled range (MRR) test and two Lagrange multiplier (LM) type tests for fractional integration in small samples is examined using Monte Carlo methods. Both the GPH and MRR tests are found to be robust to moderate autoregressive moving-average components, autoregressive conditional heteroskedasticity effects and shifts in the variance. However, these two tests are sensitive to large autoregressive moving-average components and shifts in the mean. It is also found that the LM tests are sensitive to deviations from the null hypothesis. As an illustration, the GPH test is applied to two economic data series.     

A description of phase inversion behaviour in agitated liquid-liquid dispersions under the influence of the Marangoni effect

The influence of the Marangoni effect on phase inversion behaviour is examined by integrating a microscopic study of the drop coalescence process, in which thin film drainage in the presence of insoluble surfactant occurs, into a macroscopic phase inversion model which has been developed previously using a Monte Carlo technique. This is achieved via an immobility factor, obtained from a comparison of the film drainage times for surfactant-laden systems and surfactant-free systems as a function of the drop approach velocity, surface Péclet number, initial surfactant concentration and the Hamaker constant, which is then used to modify the coalescence probability in the phase inversion model. On the one hand, the results indicate that the Marangoni effect removes any influence that the viscosity ratio has on phase inversion due to immobilisation of the interface, thus shielding the flow in the film from the effects of the flow in the dispersed phase; the point at which phase inversion occurs therefore tends towards equivolume holdups with the addition of surfactant. On the other hand, when comparisons are made with pure systems in which surfactant is absent, the system is seen to be either stabilised or de-stabilised from inversion depending on the viscosity ratio of the system. This is attributed to the influence of surfactant on the dispersion morphologies on either side of the inversion (i.e. water-in-oil dispersions and oil-in-water dispersions) and depends on the dispersed phase holdup; the Marangoni effect is felt stronger when the dispersed phase holdup is low.     

A NEW SIMULATION APPROACH TO THE ENTROPY-RELATED PROPERTIES OF FLUIDS——CHEMICAL POTENTIAL AND HELMHOLTZ FREE ENERGY OF HARD SPHERE FLUIDS

A new approach to the computation of entropy-related properties of fluids has been pre-sented.Application of the new technique to hard sphere fluids shows that it is capable of providingreliable estimates of such properties as the chemical potential and Helmholtz free energy,even athigh density where other existing methods are hardly applicable.The chemical potential of an infinitedilute component in hard sphere systems has been estimated,and compared with that calculated fromthe Carnahan-Starling equation.