Accelerated Accurate Timing Yield Estimation Based on Control Variates and Importance Sampling

Thermal-pulse method is a powerful tool for measuring space charge distributions in polymer films. The data analysis for thermal-pulse method involves the Fredholm integral equation of the first kind, which requires an appropriate numerical procedure to obtain a solution. Various numerical techniques, including scale transformation and regulation method, are proposed. Of those numerical methods, the scale transformation (ST) is the simplest and the most widely used method. However, it presents a high spatial resolution only near the sample surface. Monte Carlo (MC) method is one of the recently proposed ways to solve the equation numerically and has been successfully applied to the analysis of laser intensity modulation method data, which also involves the Fredholm integral equation of the first kind. In this paper we attempt to analyze thermal-pulse data in frequency domain with the MC method and discuss its effectiveness based on some numerical simulations. The simulation results indicate that the electric field profiles can be effectively extracted by the MC method. The computed profiles by the MC method consist well with the supposed distributions in the entire thickness of the sample, while the profiles reconstructed by the ST method fit very well to the supposed one at the vicinity of the target surface and distort sharply along the direction of the thermal pulse propagation in the sample bulk. On the other hand, the oscillations in the computed results by the MC method could deteriorate its accuracy in this study. The influence of noise level on the analysis based on the MC method is also tested by the use of the simulated data. The results show that the computed profiles would become more fluctuant as the noise level increases. This problem can be solved by selecting a larger value of tolerance during the singular value decomposition procedure. Thus, the value of tolerance is considered to be one of the key parameters in this algorithm, which is actually hard to determine. Additionally, the experimental data obtained from a polypropylene film under applied electric field are analyzed to illustrate the feasibility of MC method to be applied to the thermal-pulse experimental data. The results also show that the spatial accuracy by the MC method in the entire sample thickness is higher than by the ST method, which verifies that the MC method is more suitable for detecting the electric field distribution in the deep bulk of the sample. Owing to noise and error, the accuracy of MC calculation depends on the chosen tolerance value, which is now considered to be an obstacle in applying this method to the practical thermal-pulse measurement.

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

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.

The study addresses a problem of low-cost statistical analysis and yield optimisation of circularly polarised (CP) microstrip antennas. For the sake of computational efficiency, auxiliary response surface approximation models are utilised to establish a fast representation of the expensive full-wave electromagnetic (EM)-simulation antenna model. The surrogate permits feasible Monte Carlo (MC) analysis using a large number of random samples (necessary to maintain low variance of yield estimation). The sequential approximate optimisation is then utilised to carry out a robust design, where at each iteration, a new surrogate model is established in a relocated domain. The design objectives are set for the in-band axial ratio and impedance bandwidth. For illustration purposes, a planar CP antenna with two feed line stubs is considered. Accurate yield estimation is obtained at the cost of only a hundred of EM antenna simulations despite a large number of independent geometry parameters. Yield improvement from the initial value of 63.5% at the nominal design to 99% is achieved at the cost of 300 EM analyses. Comparison with conventional MC analysis is also provided demonstrating the accuracy of the presented approach.

A new global variance reduction technique based on pseudo flux method

Increment variance reduction techniques are add-ons to Monte Carlo (MC) simulations. They make MC simulations converging faster by repeating the number of simulations with an incremental rate derived from mathematical functions. Besides speeding up MC simulations, the major advantage of increment techniques is their ability to handle large numbers of simulations avoiding memory saturation and overflow which occur when a plain MC simulation is involved in the pricing of multi-name credit derivatives. A trend among authors pricing financial securities with MC simulation has been to choose Quasi-Monte Carlo (QMC) methods using deterministic sequences instead of MC methods involving pseudorandom generators such as congruential generator and Mersenne twister. The Increment family models circumvent the constraint of identifying the optimal QMC sequence to price a given security by using a common generator such as Matlab-LCG-Xor RNG and determining the optimal mathematical function of incrementation of MC simulations that will make the pricing of the security adequate. Market participants in need of selecting a reliable numerical method for pricing complex financial securities such as multi-name credit derivatives will find our paper appealing.

Modified efficiency importance sampling (MEIS), an importance sampling technique which can be used to yield a significant saving of run time for the assessment of bit error rate (BER) in digital communication systems using computer simulation, is described. The concept of equivalent noise source is introduced to avoid the effect of system memory on the efficiency of importance sampling, and a nonGaussian probability density function (p.d.f.) is selected as the biased equivalent noise to further improve run time. MEIS has been used successfully in the simulation of M-ary quadrature amplitude modulation (MQAM) systems. The MEIS is shown to be effective in the simulation of systems with large memory length, and in mildly nonlinear systems. The experimental results show that MEIS is a great improvement over Monte Carlo (MC) methods and that is even more efficient than the efficient importance sampling (EIS) technique. >

When estimating the bit error rate (BER) of communications systems using Monte Carlo (MC) simulation, importance sampling (IS) may be a powerful method for reducing simulation runtimes. The paper presents an IS technique combined with error event simulation in order to evaluate efficiently the performance of Viterbi decoding used with a binary nonsymmetric channel and with a binary erasure channel. Two biasing approaches are employed, stationary and nonstationary models. Comparative results between the two models and traditional MC methods are presented.

The authors extend the formulation for both classical Monte Carlo (MC) and importance sampling (IS) techniques to include the bit error rate (BER) and symbol error rate (SER) of multilevel systems based on symbol by symbol observation. A new IS technique and analysis of BER and SER based on the extended formulation are presented. The authors briefly summarize the previous work on BER of binary systems. The extended formulation is then presented. The conventional IS technique for BER of binary systems is shown to be applicable in simulating BER and SER of M-ary systems, and a new improved IS technique is presented. Numerical results for all the methods are provided. >

Simulation of particle transport is critical for a great many of scientific and engineering domains. The Monte Carlo (MC) method is one of the most important numerical methods for the simulation of particle transport, and can simulate many complex types of particle transport. But the computation requirement of the MC simulation is very large. In 2010, Intel announced the Intel Many Integrated Core (MIC) architecture, which consists of many simple general-purpose cores and supports the well-known shared-memory execution model that is the base of most nodes in HPC machines. On account of the independence of simulation of each particle in the MC method, it is well-suited to accelerate the MC simulation on MIC. In this paper, an algorithm named MCNP-MIC based MIC is presented for MC simulation of neutron transport in the context of deep penetration problem, which includes the development of parallel random generator, the assignment of particle number based thread number and the design of high efficiency data structures for parallelism. Eventually, we get the results as follows: with the same problem scale and computational accuracy, the MCNPMIC algorithm has achieved roughly 5.6-fold speedup running on a 57-core MIC chip in comparison with the serial MCNP algorithm on an Intel Xeon E5-2670 CPU.

Background Small megavoltage photon fields are increasingly used in modern radiotherapy techniques such as stereotactic radiotherapy. Therefore, it is important to study the reliability of dosimetry in the small-field conditions. The IBA Razor Nano Chamber (Nano chamber) ionization chamber is particularly intended for small-field measurements. In this work, properties of the Nano chamber were studied with both measurements and Monte Carlo (MC) simulations. Material and methods The measurements and MC simulations were performed with 6 MV, 6 MV FFF and 10 MV FFF photon beams from the Varian TrueBeam linear accelerator. The source-to-surface distance was fixed at 100 cm. The measurements and MC simulations included profiles, percentage depth doses (PDD), and output factors (OF) in square jaw-collimated fields. The MC simulations were performed with the EGSnrc software system in a large water phantom. Results The measured profiles and PDDs obtained with the Nano chamber were compared against IBA Razor Diode, PTW microDiamond and the PTW Semiflex ionization chamber. These results indicate that the Nano chamber is a high-resolution detector and thus suitable for small field profile measurements down to field sizes 2 × 2 cm2 and appropriate for the PDD measurements. The field output correction factors and field OFs were determined according to TRS-483 protocol In the 6 MV FF and FFF beams, the determined correction factors were within 1.2% for the field sizes of 1 × 1 cm2–3 × 3 cm2 and the experimental and MC defined field output factors showed good agreement. Conclusion The Nano chamber with its small cavity volume is a potential detector for the small-field dosimetry. In this study, the properties of this detector were characterized with measurements and MC simulations. The determined correction factors are novel results for the NC in the TrueBeam fields.

The basic theory of importance sampling (IS) as relevant to polarization-mode dispersion (PMD) in optical fibers is discussed, and its application to Monte Carlo (MC) simulations of PMD-induced transmission impairments is demonstrated. The use of IS allows rare PMD events to be simulated much more efficiently than with standard MC methods. As a consequence, methods employing IS provide natural and effective tools to assess PMD-induced impairments and outages in optical transmission systems at realistic probability levels.

Purpose: To create a Monte Carlo (MC) model of an ocular proton therapy device, or ocular nozzle, that can predict relative doses to within 3% or 0.5 mm, D/MU values, and be used to develop and commission an analytical algorithm to predict doses and D/MU values to within similar criteria. Methods and Materials: Depth dose profiles and D/MU values were measured in eight ocular proton therapy fields including four unmodulated and four modulated beams using a parallel‐plane ionization chamber in water. Crossfield profiles were measured at three or more depths for each of the modulated beams using film. A MC model of the ocular nozzle was constructed using the MCNPX radiation transport code. After benchmark tests against the measurements, the MC model was used to provide dosimetric data needed to develop a broad‐beam algorithm capable of predicting relative and absolute doses and to test the algorithm's predictions more comprehensively than could be afforded with measured data. Specifically, MC and analytical predictions were calculated and compared in two‐dimensions in a water phantom and in an anthropomorphic model of the eye. Results: Relative depth dose profiles between MC and measurements agreed to within 3% or 0.5 mm. MC predicted D/MU values agreed to within 1% of the measured values. Similarly, the analytical algorithm accurately predicted dose distributions where the predictions were generally within 3% or 0.5 mm of measured and simulated values at water depth > 6 mm. At shallower depths, the analytical model underestimated the dose by approximately 3% to 6%, which MC simulations revealed was due to edge‐scattered protons from the nozzle's collimators. Conclusion: The MC model accurately predicted dose distributions and D/MU values in ocular proton therapy beams. Furthermore, the present work demonstrates the value of the MC method for developing and testing contemporary analytical dose algorithms.

Simulation-based validation methods exhibit properties which should allow them to contribute to the release of highly automated driving functions (HADF). Monte-Carlo (MC) simulations make it possible to generate statistical statements about a HADF. However, the fact that accidents happen very rarely in the real world can strongly enlarge the number of MC simulation runs which are needed to obtain statistically stable results. In the past, importance sampling (IS) was used to reduce these simulation costs. This paper considers some of the still existent limitations of IS: The definition of proper safety metrics needed to find good IS distributions and the application of IS to high dimensional parameter spaces. The approach in this paper was able to reduce an IS optimization of 2700 dimensions to 17 optimizations of 9 dimensions. The number of MC runs could be reduced by a factor of 350.

In these days, Monte Carlo (MC) simulation is a method that can calculate the radiation dose that occurs in an environment in the most accurate way. The correct measurement of the dose occurring on the patient’s surface is of great importance to estimate the reactions that may occur on the patient’s skin. This importance encouraged us to do this study. The aim of this study is to determine buildup region and surface doses using MC simulation and to compare them with results of the parallel plane ion chamber and Treatment Planning System (TPS) measurements for 6-MV photon beams. Surface doses normalized to the maximum dose for the parallel plane ion chamber, MC simulation, fast photon (FP) algorithm, and collapsed cone convolution superposition (CC) algorithm are 13.6%, 30.28%, 0%, and 27.33%, respectively. The CC algorithm and parallel plane ion chamber measurements are compatible with MC simulation but the FP algorithm has calculated the dose less to a depth of 0.8 cm. Measuring the surface dose and the doses in the buildup region is of great importance in terms of accurately predicting the complications that may occur in the patient’s skin and taking precautions early. Using some methods and correction factors, the surface dose and the doses that may occur in the buildup region can be accurately calculated. It is recommended not to use the FP algorithm for stereotactic body radiation therapy and intensity-modulated radiation therapy treatments, as it cannot calculate doses correctly in the buildup region and surface.