Fast Simulated Algorithm Research Articles

Lateral Distribution Function Estimation of Electrons and Muons using Nishimura-Kamata-Greisen Function

Abstract The density of charged particles in extensive air showers reaching the surface of the Earth was calculated by estimating the lateral distribution function (LDF) of different primary particles at high energies. LDF simulation was performed using the AIRES system (version 19.04.10), a set of programs and subroutines designed to simulate ultra-high-energy air showers resulting from the interaction of cosmic rays with the Earth’s atmosphere. This system includes algorithms for fast simulation and output data management, and can simulate particle showers realistically and manage the related data efficiently. Its aim is to contribute to research on high-energy cosmic ray interactions for two charged particles, like muons and electrons, at very high energies (1016, 1018, and 1019 eV) and taking into account the effect of particles, such as protons, helium nuclei, and iron nuclei, and primary energies and zenith angles (0°, 20°, and 40°). The LDF was also calculated using the Nishimura–Kamata–Greisen function, and good agreement was found with the results produced by the AIRES system for high-energy muons and electrons created by primary particles.

On the connections between the spatial Lambda–Fleming–Viot model and other processes for analysing geo-referenced genetic data

The introduction of the spatial Lambda-Fleming–Viot model (ΛV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (Barton et al., 2010; Barton et al., 2013). The ΛV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the “pain in the torus” issue with Wright and Malécot’s isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the ΛV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the ΛV whereby lineages move rapidly over small distances. Using simulations, we show that the induced ΛV tree-generating process is well approximated by a birth–death model. Our results also indicate that Brownian motions modelling the movements of lines of descent along birth–death trees do not generally provide a good approximation of the ΛV due to habitat boundaries effects that play an increasingly important role in the long run. Accounting for habitat boundaries through reflected Brownian motions considerably increases the similarity to the ΛV model however. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the ΛV model.

A hybrid metaheuristic algorithm for scheduling iron ore reclaiming in ports

ABSTRACT This work deals with a scheduling problem of reclaimers. This problem involves a set of ships to be loaded with predefined stockpiles. These stockpiles are unloaded into ship holds, and each hold must store a predefined product and quantity of iron ore. Stockpiles are stored in storage yards, which have reclaimers to reclaim iron ore from stockpiles and send it to berthed ships. The objective is to schedule the operations of reclaimers to minimize the sum of ships' berthing times. A hybrid algorithm, combining the multi-start, GRASP and variable neighbourhood descent procedures, is proposed to treat instances of any scale of the problem. It was tested in real instances, and its results were compared with the hybrid simulated annealing algorithm from the literature and a fast simulation algorithm that emulates operators' decision-making. The proposed algorithm was the best in all instances, and statistical tests proved its superiority

Functional central limit theorems for rough volatility

The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker’s approximation of Brownian motion to the fractional Brownian case with arbitrary Hurst exponent H∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$H \\in (0,1)$\\end{document}. Some of the most relevant consequences of this ‘rough Donsker (rDonsker) theorem’ are functional weak convergence results in Skorokhod space for discrete approximations of a large class of rough stochastic volatility models. This justifies the validity of simple and easy-to-implement Monte Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark hybrid scheme and find remarkable agreement (for a large range of values of H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$H$\\end{document}). Our rDonsker theorem further provides a weak convergence proof for the hybrid scheme itself and allows constructing binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan options.

Model order reduction, a novel method using krylov sub-spaces and genetic algorithm

Model Order Reduction (MOR) of complex and large systems in Electrical engineering, continuous to be an attractive field for Engineers and Scientists over the last few decades, this complexity of models makes the control designs and simulation using Computer Aided Design (CAD) more and more difficult and consuming a lot of time. There for, accurate, robust and fast algorithms for simulation are needed. The goal of MOR is to replace the original system by an appropriate reduced system which preserves the main properties of the original one such that stability and passivity. Several analytical MOR techniques have been proposed in the literature over the past few decades, to approximate high order linear dynamic systems like Krylov sub-space techniques and SVD (Singular Value Decomposition) techniques. However, most of these techniques lead to computationally demanding, time consuming, iterative procedures that usually result in non-robustly stable models with poor frequency response resemblance to the original high order model in some frequency ranges. Recently a set of new techniques based on Artificial Intelligence (AI) were proposed in [1] for MOR. This article considers the problem of model order reduction of Linear Time In varying (LTI) systems. It is described by first and second order ordinary differential equations model. A tow steps method for model order reduction of LTI systems is proposed here, which combined features of an analytic technique (Krylov approach) and an AI technique (Genetic Algorithm). In the first step, the size of the original model is reduced to an intermediate order, using an analytical technique based on Krylov sub-spaces. In the final step of the reduction process, an AI approach based on Genetic Algorithm (GA) is applied to obtain an optimized nominal model.

Deep Generative Models for Fast Photon Shower Simulation in ATLAS

The need for large-scale production of highly accurate simulated event samples for the extensive physics programme of the ATLAS experiment at the Large Hadron Collider motivates the development of new simulation techniques. Building on the recent success of deep learning algorithms, variational autoencoders and generative adversarial networks are investigated for modelling the response of the central region of the ATLAS electromagnetic calorimeter to photons of various energies. The properties of synthesised showers are compared with showers from a full detector simulation using geant4. Both variational autoencoders and generative adversarial networks are capable of quickly simulating electromagnetic showers with correct total energies and stochasticity, though the modelling of some shower shape distributions requires more refinement. This feasibility study demonstrates the potential of using such algorithms for ATLAS fast calorimeter simulation in the future and shows a possible way to complement current simulation techniques.

Algorithms for Fast Spiking Neural Network Simulation on FPGAs

Algorithms for Fast Spiking Neural Network Simulation on FPGAs

A fast algorithm for simulation and analysis of wavefields in acoustic single-well imaging of logging-while-drilling considering arbitrary types of sources

Acoustic single-well imaging (SWI) of logging-while-drilling (LWD) is an advanced logging method in reservoir exploration, which uses reflected waves to detect the around-borehole geologic structures and quickly determines the drilling direction for enhancing the drilling-encounter ratio and reducing the drilling risk. Forward acoustic modeling is a fundamental problem for SWI in LWD. Due to the complex structures, it is a challenge to simulate the wave propagation and investigate wavefield characteristics based on the forward model. Numerical modeling is a commonly used method for calculating wavefields; however, it is too computationally expensive. In this study, we develop a fast method for calculating the full reflected pressure and displacement waves (i.e., P-P, SV-SV, SH-SH, and P-SV/SV-P) in SWI of LWD considering different types of sources such as arcuate, monopole, and dipole transmitters. The analytical algorithm is developed by applying the reciprocity relation between the virtual force (displacement) sources located at the receiver position and the outside-borehole virtual forces that are equivalent to the reflections from the formation interfaces. Numerical experiments indicate that the analytical solutions agree well with the reference solutions from the 3D finite-difference time-domain method, demonstrating the accuracy and high efficiency of the analytical method. Based on the analytical solutions, we find that LWD reflected waves are much more sensitive to the azimuth than those in the wireline case, indicating that the availability of LWD is important for identifying the reflector azimuth. Furthermore, to enhance the reception efficiency of reflected waves, the LWD parameters are optimized. For slow formations, we suggest using a dipole source with dominant excitation-frequency band being from 1 kHz to 3 kHz. For fast formations, a dipole with wider excitation-frequency band from 1 kHz to 5 kHz is recommended. For all formations, recording pressure signals indicates much higher reception efficiency than the displacement signals.

High-Precision GPU-Accelerated Simulation Algorithm for Targets under Non-Uniform Cluttered Backgrounds

This article presents a high-precision airborne video synthetic aperture radar (SAR) raw echo simulation method aimed at addressing the issue of simulation accuracy in video SAR image generation. The proposed method employs separate techniques for simulating targets and ground clutter, utilizing pre-existing SAR images for clutter simulation and employing the shooting and bouncing rays (SBR) approach to generate target echoes. Additionally, the method accounts for target-generated shadows to enhance the realism of the simulation results. The fast simulation algorithm is implemented using the C++ programming language and the Accelerated Massive Parallelism (AMP) framework, providing a fusion technique for integrating clutter and target simulations. By combining the two types of simulated data to form the final SAR image, the method achieves efficient and accurate simulation technology. Experimental results demonstrate that this method not only improves computational speed but also ensures the accuracy and stability of the simulation outcomes. This research holds significant implications for the development of algorithms pertaining to video SAR target detection and tracking, providing robust support for practical applications.

An improved Z-MAP method based on the SQP algorithm for fast surface topography simulation of ball-end milling

An improved Z-MAP method based on the SQP algorithm for fast surface topography simulation of ball-end milling

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually in physical space using iterative solvers, and the resulting pressure gradient is then applied to make the velocity field divergence-free. It is generally accepted that this pressure-correction stage is the most time-consuming part of the flow solver and any meaningful acceleration would contribute significantly to the overall computational efficiency. The objective of the present work was to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretisations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method, which consists of two sub-steps, was chosen for the purposes of demonstration. In the first sub-step, the momentum equations were discretised on unstructured grids and solved by conventional numerical methods, here a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double-discretisation system and combines the weighted least-squares approximation with the essence of immersed boundary methods. Such a design allowed us to develop an FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of the boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. The numerical experiments of five test cases were performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results showed that the new FFT-based hybrid algorithm works and is robust, and it was significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows.

Immediate Transitions in Timed Continuous Petri Nets: Performance Evaluation and Control

Timed continuous Petri nets (TCPNs) are continuous-state dynamical systems that were originally defined to approximate the behavior of timed discrete event systems. In particular, it has been shown in the literature that TCPNs approximate the average marking and throughput of a class of generalized stochastic Petri nets (GSPNs), a well-known model used for the performance evaluation analysis of manufacturing, communication, logistic and traffic systems, among others. In this work, the TCPN model is enriched with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">immediate transitions</i> , which represent very fast events, resulting in a new model denoted as TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I. Then, a fast simulation algorithm for TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> Is is introduced. Nevertheless, the introduction of continuous immediate transitions leads to ill-conditioned problems when analyzing the TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I model. For such reason, a couple of procedures are, here, introduced to transform a TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I model into a set of dynamically equivalent TCPNs, by removing the immediate transitions, allowing, thus, the application of analysis techniques and methods already proposed in the literature for TCPN systems. The application of the results introduced in this work for performance evaluation and model predictive control is illustrated through a manufacturing example.

Numerical Analysis of Transient State Heat Transfer by Spectral Method Based on POD Reduced-Order Extrapolation Algorithm

In order to meet the requirements of high accuracy and fast algorithm for numerical heat transfer simulation, an iterative scheme of Proper Orthogonal Decomposition (for short, POD) dimension reduction based on the classical central difference Galerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. The POD dimension reduction spectral method model is constructed by taking the calculation results of classical central difference Galerkin spectral method as sample data. The numerical algorithm characteristics of flow and heat transfer are studied by using a partial differential equation as a mathematical model, and the error estimation is given. Finally, different time intervals are used as parameters to simulate experiments. The results show that the POD method is applicable to transient nonlinear heat conduction problems, and the maximum average relative error of the reconstructed temperature field is 0.89675%. Moreover, the POD method not only has a high calculation accuracy, but also has an average calculation speed as high as 310.25 times that of the central difference Galerkin algorithm. It can be seen that under the condition that the error between the solution of POD dimension reduction extrapolation algorithm and the solution of classical central difference Galerkin spectrum method is small enough, the POD method can greatly reduce the calculation amount, shorten the running time, and ensure a high accuracy of the calculation results, thus verifying the effectiveness and feasibility of the algorithm.

QuDiet: A classical simulation platform for qubit‐qudit hybrid quantum systems

AbstractIn recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state‐of‐the‐art classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higher‐dimensional quantum computing systems. Through recent developments in higher‐dimensional quantum computing systems, it is realised that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, QuDiet, a state‐of‐the‐art user‐friendly python‐based higher‐dimensional quantum computing simulator is introduced. QuDiet offers multi‐valued logic operations by utilising generalised quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. Various benchmark quantum circuits is simulated in QuDiet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, QuDiet provides a full qubit‐qudit hybrid quantum simulator package with quantum circuit templates of well‐known quantum algorithms for fast prototyping and simulation. Comprehensive simulation up to 20 qutrits circuit on depth 80 on QuDiet was successfully achieved. The complete code and packages of QuDiet is available at https://github.com/LegacYFTw/QuDiet.

Development of a fast and stable dynamics algorithm for soft robots including viscoelastic body

In recent years, research and development of robots that exist in the same space as humans and can collaborate with humans have been actively carried out. If the body of a robot is made of a hard material, it may cause injury. Therefore, attempts have been made to make a robot with a soft body using rubber or resin. In order to accelerate such research on soft robotics, it is necessary to establish fast and stable simulation algorithm for robots containing viscoelastic bodies such as rubber and resin. Therefore, in this study, we consider to approximate viscoelastic bodies with finite rigid body segments and connect them with joints and linear viscoelastic elements such as Voigt model, Maxwell model and generalized Maxwell model to approximate viscoelastic properties. The recursive dynamics algorithm is used to speed up the calculation, and the generalized-α method is used to stabilize the numerical integration. In particular, we propose a new method on how to incorporate the Maxwell model and generalized Maxwell model into recursive dynamics algorithm and generalized-α method. The effectiveness of the proposed method is confirmed by some numerical examples. In addition, the effectiveness of the proposed method is verified on a real system by applying Particle Swarm Optimization (PSO) to identify the dynamic parameters in linear viscoelastic elements.

An Algorithm for Fast Simulation of CW Illuminator

The continuous wave (CW) illuminator is aimed to simulate high-altitude nuclear electromagnetic pulse. In this article, a simulation algorithm is proposed covering the method of moments and finite difference method (FDM), with the high-speed simulation of the CW illuminator with arbitrary ellipse size, arbitrary loading, and arbitrary polarization direction. Based on the surface electric field equation of the CW illuminator, the mathematical model is established with the vector potential equation and the boundary conditions. In this model, the pulse function and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> function are set as the basis function and the weight function, respectively, for the establishment of the current equation, with the current distribution determined by the simplification equation with image theory and nonuniform FDM. Finally, as the field distribution is determined by the superposition theorem. The simulation algorithm is verified by the self-built CW illuminator.

Uncertainties in Electric Circuit Analysis of Anisotropic Electrical Conductivity and Piezoresistivity of Carbon Nanotube Nanocomposites.

Electrical conductivity and piezoresistivity of carbon nanotube (CNT) nanocomposites are analyzed by nodal analysis for aligned and random CNT networks dependent on the intrinsic CNT conductivity and tunneling barrier values. In the literature, these parameters are assigned with significant uncertainty; often, the intrinsic resistivity is neglected. We analyze the variability of homogenized conductivity, its sensitivity to deformation, and the validity of the assumption of zero intrinsic resistivity. A fast algorithm for simulation of a gauge factor is proposed. The modelling shows: (1) the uncertainty of homogenization caused by the uncertainty in CNT electrical properties is higher than the uncertainty, caused by the nanocomposite randomness; (2) for defect-prone nanotubes (intrinsic conductivity ~104 S/m), the influence of tunneling barrier energy on both the homogenized conductivity and gauge factor is weak, but it becomes stronger for CNTs with higher intrinsic conductivity; (3) the assumption of infinite intrinsic conductivity (defect-free nanotubes) has strong influence on the homogenized conductivity.

Community integration algorithms (CIAs) for dynamical systems on networks

Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation of large network models is often computationally prohibitive. Yet, most networks have intrinsic community structure. We exploit these communities and propose a fast simulation algorithm for network dynamics. In particular, aggregating the inputs a node receives constitutes the limiting factor in numerically simulating large-scale network dynamics. We develop community integration algorithms (CIAs) significantly reducing function-evaluations. We obtain a substantial reduction from polynomial to linear computational complexity. We illustrate our results in multiple applications including classical and higher-order Kuramoto-type systems for synchronisation and Cucker–Smale systems exhibiting flocking behaviour on synthetic as well as real-world networks. Numerical comparison and theoretical analysis confirm the robustness and efficiency of CIAs.

Matérn process-based simulation of wind speed time series

This work proposes a practical methodological framework for simulating long-term discrete wind speed time series, for applications to renewable energy systems. The framework is based on the Matérn stochastic process, that is used to identify and extract the short and long-term periodic components present in the mean and variance of a wind speed time series, and to characterize the residual random component. The procedure of construction of synthetic wind speed time series is developed, rooted in a fast numerical simulation algorithm for the Matérn process. We empirically validate the usefulness of the proposed framework by numerical experiments based on three real historical wind speed datasets. The results show consistent statistical similarities between the historical and simulated wind speed time series of data.

Robust SAV-Ensemble algorithms for parametrized flow problems with energy stable open boundary conditions

In this report we propose fast and robust ensemble simulation algorithms for parametrized nonlinear flow problems with open boundaries. We synthesize the recent SAV idea, the ensemble timestepping and the energy stable open boundary conditions, and develop efficient ensemble algorithms that only require a single matrix assembly for all realizations and all time steps. Moreover, the proposed algorithms are unconditionally stable without any restricting assumptions on the variance of the viscosities or the time steps, and they always produce positive values for the auxiliary variables. The second order algorithm is numerically tested on three benchmark flow problems with open boundaries, and is shown to be both accurate and effective in preventing the backflow instabilities.