Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation

The semiclassical (SC) initial value representation (IVR) for the time evolution operator e−iĤt/ℏ involves a phase space integral over the initial conditions of classical trajectories. It is shown in this paper how an IVR for the two time evolution operators in a typical quantum mechanical time correlation function, CAB(t)≡tr[ÂeiĤt/ℏB̂e−iĤt/ℏ], can be combined into one such phase space integral; i.e., time evolution from 0 to t and from t to 0 is combined into one overall SC-IVR propagation. This not only reduces the dimensionality of the phase space average, but the forward–backward (FB) nature of the net trajectory has a partial self-cancellation that reduces the oscillatory behavior of the integrand. Several applications of this FB-IVR to reactive flux correlation functions are presented to illustrate its possibilities.

Within a differential expression of the Heisenberg operator, the forward and backward evolution can be joined together along a closed time contour. This manipulation leads to a dramatic cancellation of oscillations due to the two individual propagators in the Heisenberg operator and the resulting forward-backward propagator is more tractable to semiclassical approximations. This article gives a detailed description of the forward-backward semiclassical dynamics (FBSD) formalism. The semiclassical propagators, especially those of the initial value representations (IVRs), are briefly discussed. The derivation of the FBSD based on the Herman–Kluk propagator is reviewed. Different FBSD formulations with other semiclassical IVRs are worked out and numerical calculations show that they are also capable of describing quantum dynamics semiquantitatively and all display accuracy similar to the classical Wigner method.

Ultra-high performance concrete has excellent mechanical properties such as ultra-high strength and high durability, and has a broad application prospect in the field of bridge engineering. To make full use of the superior mechanical properties of UHPC and reduce the cost of the bridge, the particle swarm optimization algorithm is used to optimize the structural design of the UHPC beam bridge; Aiming at the problem that the traditional particle swarm optimization algorithm is easy to fall into local optimum, the nonlinear adaptive weight update method is used to improve the particle swarm optimization algorithm. Based on the above-mentioned improved particle swarm optimization algorithm, the optimal design method of ordinary reinforced UHPC beams and prestressed UHPC beams with commonly used highway spans is studied. The reliability of the optimized structural limit state is analyzed by Monte Carlo (MC) importance sampling method. The results show that compared with the traditional particle swarm optimization algorithm, the improved particle swarm optimization algorithm has higher convergence speed and convergence accuracy. The optimal height-span ratio of ordinary reinforced UHPC beams decreases with the increase of the span, and the construction cost gradually increases; The optimal height-span ratio of the prestressed beam decreases first and then increases with the increase of the span, and the construction cost gradually increases. The calculation results of load capacity reliability indexes of optimization results are all higher than the target reliability indexes of similar components stipulated in China’s “Uniform Standard for Structural Reliability Design of Highway Engineering”.

In this paper, we present a variance minimization (VM) procedure for rare event simulation in tandem queueing networks. We prove that the VM method can produce a zero variance. The VM method is suitable to compute optimal importance sampling (IS) parameters for small scale tandem networks. For large scale tandem networks we propose a sub-optimal IS (SOIS) method, which projects the optimal biased transition probabilities of the corresponding small scale system into those of a large scale system. In other words, we establish an efficient IS method for a large scale system by zooming into a small scale system and then projecting our findings into the large scale system. The numerical results show that our SOIS method can produce accurate results with very short CPU time, while many other methods often require much longer.

Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of this proposal is key for achieving a high performance. In adaptive IS (AIS) methods, a set of proposals is iteratively improved. AIS is a relevant and timely methodology although many limitations remain yet to be overcome, e.g., the curse of dimensionality in high-dimensional and multi-modal problems. Moreover, the Hamiltonian Monte Carlo (HMC) algorithm has become increasingly popular in machine learning and statistics. HMC has several appealing features such as its exploratory behavior, especially in high-dimensional targets, when other methods suffer. In this letter, we introduce the novel Hamiltonian adaptive importance sampling (HAIS) method. HAIS implements a two-step adaptive process with parallel HMC chains that cooperate at each iteration. The proposed HAIS efficiently adapts a population of proposals, extracting the advantages of HMC. HAIS can be understood as a particular instance of the generic layered AIS family with an additional resampling step. HAIS achieves a significant performance improvement in high-dimensional problems w.r.t. state-of-the-art algorithms. We discuss the statistical properties of HAIS and show its high performance in two challenging examples.

Massively repeated structures such as SRAM cells usually require extremely low failure rate. This brings on a challenging issue for Monte Carlo based statistical yield analysis, as huge amount of samples have to be drawn in order to observe one single failure. Fast Monte Carlo methods, e.g. importance sampling methods, are still quite expensive as the anticipated failure rate is very low. In this paper, a new method is proposed to tackle this issue. The key idea is to improve traditional importance sampling method with an efficient online surrogate model. The proposed method improves the performance for both stages in importance sampling, i.e. finding the distorted probability density function, and the distorted sampling. Experimental results show that the proposed method is 1e2X∼1e5X faster than the standard Monte Carlo approach and achieves 5X∼22X speedup over existing state-of-the-art techniques without sacrificing estimation accuracy.

The study of quantum stochastic processes presents severe difficulties, both on the theory level as well as on technical grounds. The numerically exact solution remains prohibitive even today. In this paper we review and present new results for three different methods used for the modelling of quantum stochastic processes. These include a mixed quantum classical approach, semiclassical initial value representations of the quantum propagator and the reduced density matrix approach as typified by the quantum Wigner-Fokker-Planck equation. A new semiclassical initial value representation that does away with cumbersome prefactors which depend on the monodromy matrix elements but is exact for a harmonic oscillator is presented and its properties analysed. A recently proposed systematic method for improving semiclassical initial value representations is reviewed. The generalization of the Wigner-Fokker-Planck equation to stochastic processes with memory is obtained by using a novel integral equation representation.

Estimating the distribution of total default losses on the Spanish financial system

This paper illustrates the use of the Importance Sampling (IS) technique for efficient simulation of Orthogonal Frequency Division Multiplexing Systems operating over frequency selective fading channels with equalization. In order to achieve higher estimator variance reduction gains, the proper biasing procedure for time domain noise density function and the way of un-biasing the error count at the receiver in frequency domain are shown. Further, the optimum biasing parameters for conventional importance sampling (CIS) and improved importance sampling (IIS) methods are obtained. It is demonstrated, through simulations, that the proposed methods can provide extensive gains in estimator variance reduction and runtime saving compared to the conventional Monte-Carlo (MC) simulations.

Estimation of extreme response values is very important for structural design of wind turbines. Due to the influence of control system and nonlinear structural behavior the extreme response is usually assessed based on simulation of turbulence time series. In this paper the problem of statistical load extrapolation is considered using techniques from structural reliability theory. Different simulation techniques to estimate extreme response characteristics are described and compared, including crude Monte Carlo simulation, Importance Sampling, and splitting methods such as the Russian Roulette and the Double and Clump algorithm. A statistically consistent technique is described for including statistical uncertainty and assessing the extreme 50-year response using simulated time series and conditioned on the model parameters. The peak over threshold method together with the Maximum Likelihood Method provides a tool to obtain consistent estimates incl. the statistical uncertainty. An illustrative example indicates that the statistical uncertainty is important compared to the coefficient of variation of the extreme response when the number of 10 minutes simulations at each mean wind speed is limited to 10.

To reduce the substantial leakage current, the supply voltage of SRAM cells has being scaled down towards its lower limit, which is called the data Retention Voltage (DRV). Although the power consumption is largely reduced, this down-scaling trend, however, impacts the stability of the SRAM cell due to the unpredictable process or device parameter variations. In this work, we propose a novel method to evaluate the DRV of SRAM cells at the presence of variations. The DRV issue is first formulated as a time domain worst performance bound problem. To accurately and efficiently evaluate the DRV, a multi-start point (MSP) optimization strategy is then studied and developed with the use of practical circuit simulator. One feature of the proposed method is that it can efficiently evaluate the DRV without suffering from any process/model accuracy. Experiment results show that it achieves a speedup of 3 and 5-7 order over the Importance Sampling (IS) and Monte Carlo (MC) method respectively under the context of the DRV evaluation in this paper. The proposed method can serve as an efficient DRV evaluation tool on any specific technology process or in-house circuit simulator. In this work, the DRVs at the technology node from 130 nm to 45 nm under the influence of different variation sources are also presented and analyzed.

In this paper we propose a new importance sampling (IS) scheme to estimate the low error-rate performance of LDPC codes over a Rayleigh fading channel. It biases the Rayleigh fading distribution as well as the noise distribution in order to improve the quality of estimation. The proposed IS scheme is compared with the Monte-Carlo (MC) simulator and other IS schemes in terms of its efficiency and accuracy. Numerical results show that the proposed IS estimator is much more efficient than the MC estimator and other IS estimators from the viewpoint of the required simulation time. Furthermore, the proposed IS scheme provides a more accurate performance estimation of LDPC codes over a Rayleigh fading channel with only a limited simulation time than other IS schemes.

An importance sampling (IS) simulation method is developed for evaluating the bit-error rate of one-shot and recursive Bayesian equalizers (symbol-by-symbol detectors.) It is shown that the one-shot Bayesian equalizer structure closely resembles that of a multi-user detector for CDMA. Hence, noise biasing IS methods developed previously for CDMA detectors should also be appropriate for Bayesian equalizers. At low SNRs, the decision boundary far the one-shot Bayesian equalizer approaches a hyperplane. This hyperplane is viewed as an approximation to the true decision boundary at high SNRs, and can thus be used to construct an appropriate noise bias vector. With a slight modification, it is shown that the IS technique for the one-shot Bayesian equalizer can also be applied to the Abend and Fritchman (1970) recursive algorithm, and finally, to an adaptive Bayesian blind equalizer. IS simulations are carried out for both the nonadaptive Bayesian equalizers and for the blind recursive equalizer. >

Analysis of inconsistent source sampling in monte carlo weight-window variance reduction methods

Vehicle routing problem belongs to classical Combination Optimization hard problem and has been extensively studied by many researchers. Vehicle Routing Problem with Weight Coefficients and Stochastic Demands (WVRPSD) is established and a new implementation for importance sampling method to solve this model is proposed in this paper, in which the classical exponential change of measure is adopted to construct the family of importance sampling distributions, and the optimal importance sampling distribution is obtained by minimizing the variance of importance sampling estimator. Numerical experiments have been conducted and the results indicate that the method can effectively solve this problem.