Articles de revues : « Stochastic simulation algorithms »

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Stutz, Timothy C., Alfonso Landeros, Jason Xu, Janet S. Sinsheimer, Mary Sehl, and Kenneth Lange. "Stochastic simulation algorithms for Interacting Particle Systems." PLOS ONE 16, no. 3 (2021): e0247046. http://dx.doi.org/10.1371/journal.pone.0247046.

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Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.

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Mooasvi, Azam, and Adrian Sandu. "APPROXIMATE EXPONENTIAL ALGORITHMS TO SOLVE THE CHEMICAL MASTER EQUATION." Mathematical Modelling and Analysis 20, no. 3 (2015): 382–95. http://dx.doi.org/10.3846/13926292.2015.1048760.

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This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.

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Altıntan, Derya, Vi̇lda Purutçuoğlu, and Ömür Uğur. "Impulsive Expressions in Stochastic Simulation Algorithms." International Journal of Computational Methods 15, no. 01 (2017): 1750075. http://dx.doi.org/10.1142/s021987621750075x.

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Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.

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Konopel'kin, M. Yu, S. V. Petrov, and D. A. Smirnyagina. "Implementation of stochastic signal processing algorithms in radar CAD." Russian Technological Journal 10, no. 5 (2022): 49–59. http://dx.doi.org/10.32362/2500-316x-2022-10-5-49-59.

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Objectives. In 2020, development work on the creation of a Russian computer-assisted design system for radars (radar CAD) was completed. Radar CAD provides extensive opportunities for creating simulation models for developing the hardware-software complex of radar algorithms, which take into account the specific conditions of aerospace environment observation. The purpose of the present work is to review and demonstrate the capabilities of radar CAD in terms of implementing and testing algorithms for processing stochastic signals.Methods. The work is based on the mathematical apparatus of linear algebra. Analysis of algorithms characteristics was carried out using the simulation method.Results. A simulation model of a sector surveillance radar with a digital antenna array was created in the radar CAD visual functional editor. The passive channel included the following algorithms: algorithm for detecting stochastic signals; algorithm for estimating the number of stochastic signals; direction finding algorithm for stochastic signal sources; adaptive spatial filtering algorithm. In the process of simulation, the algorithms for detecting and estimating the number of stochastic signals produced a correct detection sign and an estimate of the number of signals. The direction-finding algorithm estimated the angular position of the sources with an accuracy of fractions of degrees. The adaptive spatial filtering algorithm suppressed interfering signals to a level below the antenna's intrinsic noise power.Conclusions. The processing of various types of signals can be simulated in detail on the basis of the Russian radar CAD system for the development of functional radar models. According to the results of the simulation, coordinates of observing objects were obtained and an assessment of the effectiveness of the algorithms was given. The obtained results are fully consistent with the theoretical prediction. The capabilities of radar CAD systems demonstrated in this work can be used by specialists in the field of radar and signal processing.

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Wieder, Nicolas, Rainer H. A. Fink, and Frederic von Wegner. "Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics." Journal of Biomedicine and Biotechnology 2011 (2011): 1–5. http://dx.doi.org/10.1155/2011/572492.

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In simulations of chemical systems, the main task is to find an exact or approximate solution of thechemical master equation(CME) that satisfies certain constraints with respect to computation time and accuracy. WhileBrownian motionsimulations of single molecules are often too time consuming to represent the mesoscopic level, the classicalGillespie algorithmis a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains.Gillespie's algorithmcan be approximated via thetau-leapmethod and thechemical Langevin equation(CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

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Ding, Liangliang, Jingyuan Zhou, Wenhui Tang, Xianwen Ran, and Ye Cheng. "Research on the Crushing Process of PELE Casing Material Based on the Crack-Softening Algorithm and Stochastic Failure Algorithm." Materials 11, no. 9 (2018): 1561. http://dx.doi.org/10.3390/ma11091561.

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In order to more realistically reflect the penetrating and crushing process of a PELE (Penetration with Enhanced Lateral Efficiency) projectile, the stochastic failure algorithm and crack-softening algorithm were added to the corresponding material in this paper. According to the theoretical analysis of the two algorithms, the material failure parameters (stochastic constant γ, fracture energy Gf, and tensile strength σT) were determined. Then, four sets of simulation conditions ((a) no crack softening, (b) no stochastic failure, (c) no crack softening and no stochastic failure, and (d) crack softening and stochastic failure) were designed to qualitatively describe the influences of the failure algorithms, which were simulated by the finite element analysis software AUTODYN. The qualitative comparison results indicate that the simulation results after adding the two algorithms were closer to the actual situation. Finally, ten groups of simulation conditions were designed to quantitatively analyze the coincidence degree between the simulation results and the experimental results by means of two parameters: the residual velocity of the projectile and the maximum radial velocity of fragments. The results show that the simulation results coincide well with the experimental results and the errors were small. Therefore, the ideas proposed in this paper are scientific, and the conclusions obtained can provide guidance for engineering research.

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Bhatnagar, Shalabh, Vivek Kumar Mishra, and Nandyala Hemachandra. "Stochastic Algorithms for Discrete Parameter Simulation Optimization." IEEE Transactions on Automation Science and Engineering 8, no. 4 (2011): 780–93. http://dx.doi.org/10.1109/tase.2011.2159375.

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XU, ZI, YINGYING LI, and XINGFANG ZHAO. "SIMULATION-BASED OPTIMIZATION BY NEW STOCHASTIC APPROXIMATION ALGORITHM." Asia-Pacific Journal of Operational Research 31, no. 04 (2014): 1450026. http://dx.doi.org/10.1142/s0217595914500262.

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This paper proposes one new stochastic approximation algorithm for solving simulation-based optimization problems. It employs a weighted combination of two independent current noisy gradient measurements as the iterative direction. It can be regarded as a stochastic approximation algorithm with a special matrix step size. The almost sure convergence and the asymptotic rate of convergence of the new algorithm are established. Our numerical experiments show that it outperforms the classical Robbins–Monro (RM) algorithm and several other existing algorithms for one noisy nonlinear function minimization problem, several unconstrained optimization problems and one typical simulation-based optimization problem, i.e., (s, S)-inventory problem.

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Braun, Daniel, and Ronny Müller. "Stochastic emulation of quantum algorithms." New Journal of Physics 24, no. 2 (2022): 023028. http://dx.doi.org/10.1088/1367-2630/ac4b0f.

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Abstract Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two qubits at the same time. The former aspect renders the direct classical simulation of quantum algorithms difficult. Here we introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares these basic properties of quantum mechanical states needed for a quantum algorithm. Discretization of the positions allows one to represent the quantum mechanical state of n bit qubits by 2(n bit + 1) classical stochastic bits. Based on this, we demonstrate many-particle interference and representation of pure entangled quantum states via derivatives of probability distributions and find the universal set of stochastic maps that correspond to the quantum gates in a universal gate set. We prove that the propagation via the stochastic map built from those universal stochastic maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state with the corresponding quantum algorithm, leading to an automated translation of a quantum algorithm to a stochastic classical algorithm. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of the emulation.

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Wang, Dongqing, Tong Shan, and Rui Ding. "DATA FILTERING BASED STOCHASTIC GRADIENT ALGORITHMS FOR MULTIVARIABLE CARAR-LIKE SYSTEMS." Mathematical Modelling and Analysis 18, no. 3 (2013): 374–85. http://dx.doi.org/10.3846/13926292.2013.804889.

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This paper considers identification problems for a multivariable controlled autoregressive system with autoregressive noises. A hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm are presented to estimate the parameter vectors and parameter matrix of such multivariable colored noise systems, by using the hierarchical identification principle. The simulation results show that the proposed hierarchical gradient estimation algorithms are effective.

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Hedar, Abdel-Rahman, Amira Allam, and Alaa Abdel-Hakim. "Simulation-Based EDAs for Stochastic Programming Problems." Computation 8, no. 1 (2020): 18. http://dx.doi.org/10.3390/computation8010018.

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With the rapid growth of simulation software packages, generating practical tools for simulation-based optimization has attracted a lot of interest over the last decades. In this paper, a modified method of Estimation of Distribution Algorithms (EDAs) is constructed by a combination with variable-sample techniques to deal with simulation-based optimization problems. Moreover, a new variable-sample technique is introduced to support the search process whenever the sample sizes are small, especially in the beginning of the search process. The proposed method shows efficient results by simulating several numerical experiments.

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Bhatnagar, Shalabh, N. Hemachandra, and Vivek Kumar Mishra. "Stochastic approximation algorithms for constrained optimization via simulation." ACM Transactions on Modeling and Computer Simulation 21, no. 3 (2011): 1–22. http://dx.doi.org/10.1145/1921598.1921599.

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Jeschke, Matthias, Roland Ewald, and Adelinde M. Uhrmacher. "Exploring the performance of spatial stochastic simulation algorithms." Journal of Computational Physics 230, no. 7 (2011): 2562–74. http://dx.doi.org/10.1016/j.jcp.2010.12.030.

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Xu, Wenlong. "Conditional curvilinear stochastic simulation using pixel-based algorithms." Mathematical Geology 28, no. 7 (1996): 937–49. http://dx.doi.org/10.1007/bf02066010.

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Ding, Xiaodong, and Chengliang Wang. "A Novel Algorithm of Stochastic Chance-Constrained Linear Programming and Its Application." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/139271.

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The computation problem is discussed for the stochastic chance-constrained linear programming, and a novel direct algorithm, that is, simplex algorithm based on stochastic simulation, is proposed. The considered programming problem in this paper is linear programming with chance constraints and random coefficients, and therefore the stochastic simulation is an important implement of the proposed algorithm. By theoretical analysis, the theory basis of the proposed algorithm is obtained and, by numerical examples, the feasibility and validness of this algorithm are illustrated. The detailed algorithm procedure is given, which is easily converted into the executable codes of software tools. Then, we compare it with some algorithms to verify its superiority. Finally, a practical example is presented to show its practicability.

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Tian, Heng, Fuhai Duan, Yong Sang, and Liang Fan. "Novel algorithms for sequential fault diagnosis based on greedy method." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234, no. 6 (2020): 779–92. http://dx.doi.org/10.1177/1748006x20914498.

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Test sequencing for binary systems is a nondeterministic polynomial-complete problem, where greedy algorithms have been proposed to find the solution. The traditional greedy algorithms only extract a single kind of information from the D-matrix to search the optimal test sequence, so their application scope is limited. In this study, two novel greedy algorithms that combine the weight index for fault detection with the information entropy are introduced for this problem, which are defined as the Mix1 algorithm and the Mix2 algorithm. First, the application scope for the traditional greedy algorithms is demonstrated in detail by stochastic simulation experiments. Second, two new heuristic formulas are presented, and their scale factors are determined. Third, an example is used to show how the two new algorithms work, and four real-world D-matrices are employed to validate their universality and stability. Finally, the application scope of the Mix1 and Mix2 algorithms is determined based on stochastic simulation experiments, and the two greedy algorithms are also used to improve a multistep look-ahead heuristic algorithm. The Mix1 and Mix2 algorithms can obtain good results in a reasonable time and have a wide application scope, which also can be used to improve the multistep look-ahead heuristic algorithm.

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Scholz, Klaus. "Stochastic simulation of urbanhydrological processes." Water Science and Technology 36, no. 8-9 (1997): 25–31. http://dx.doi.org/10.2166/wst.1997.0639.

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Calculations in urban hydrology have almost exclusively been of deterministic character and give therefore unequivocal results. Uncertainties, which are always present, can not been eliminated by more complex models. To take uncertainties into account stochastic algorithms are integrated into hydrological components. A stochastic-hydrological method has developed which can be used to various problems. In contrast to the usual purely deterministic models the model makes it possible to get concrete information of liability of the calibration and prognosis regarding confidence limits The model is applied for the calibration and prognosis of pollutant load hydrographs. The result is, that stochastic and physical based parameters should be taken into account.

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Ozguven, Eren Erman, and Kaan Ozbay. "Simultaneous Perturbation Stochastic Approximation Algorithm for Solving Stochastic Problems of Transportation Network Analysis." Transportation Research Record: Journal of the Transportation Research Board 2085, no. 1 (2008): 12–20. http://dx.doi.org/10.3141/2085-02.

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Stochastic optimization has become one of the important modeling approaches in transportation network analysis. For example, for traffic assignment problems based on stochastic simulation, it is necessary to use a mathematical algorithm that iteratively seeks out the optimal, the suboptimal solution, or both, because an analytical (closed-form) objective function is not available. Therefore, efficient stochastic approximation algorithms that can find optimal or suboptimal solutions to these problems are needed. The method of successive averages (MSA), a well-known algorithm, is used to solve both deterministic and stochastic equilibrium assignment problems. As found in previous studies, the MSA has questionable convergence characteristics, especially when the number of iterations is not sufficiently large. In fact, the stochastic approximation algorithm is of little practical use if the number of iterations to reduce the errors to within reasonable bounds is arbitrarily large. An efficient method to solve stochastic approximation problems is the simultaneous perturbation stochastic approximation (SPSA), which can be a viable alternative to the MSA because of its proven power to converge to sub-optimal solutions in the presence of stochasticities and its ease of implementation. The performance of MSA and SPSA algorithms is compared for solving traffic assignment problems with varying levels of stochastic-ities on a small network. The utmost importance is given to comparison of the convergence characteristics of the two algorithms as well as to the computational times. A worst-case scenario is also studied to check the efficiency and practicality of both algorithms in terms of computational times and accuracy of results.

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Kabanov, A. A., and S. A. Dubovik. "Simulation of Rare Events in Stochastic Systems." Journal of Physics: Conference Series 2096, no. 1 (2021): 012151. http://dx.doi.org/10.1088/1742-6596/2096/1/012151.

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Abstract The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.

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Luo, Jun Jie, Cheng Su, and Da Jian Han. "A Spectral Representation Model for Simulation of Multivariate Random Processes." Advanced Materials Research 368-373 (October 2011): 1253–58. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.1253.

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A model is proposed to simulate multivariate weakly stationary Gaussian stochastic processes based on the spectral representation theorem. In this model, the amplitude, phase angle, and frequency involved in the harmonic function are random so that the generated samples are real stochastic processes. Three algorithms are then adopted to improve the simulation efficiency. A uniform cubic B-spline interpolation method is employed to fit the target factorized power spectral density function curves. A recursive algorithm for the Cholesky factorization is utilized to decompose the cross-power spectral density matrices. Some redundant cosine terms are cut off to decrease the computation quantity of superposition. Finally, an example involving simulation of turbulent wind velocity fluctuations is given to validate the capability and accuracy of the proposed model as well as the efficiency of the optimal algorithms.

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Liu, Ding-Peng, Tsung-Yueh Lin, and Hsin-Haou Huang. "Improving the Computational Efficiency for Optimization of Offshore Wind Turbine Jacket Substructure by Hybrid Algorithms." Journal of Marine Science and Engineering 8, no. 8 (2020): 548. http://dx.doi.org/10.3390/jmse8080548.

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When solving real-world problems with complex simulations, utilizing stochastic algorithms integrated with a simulation model appears inefficient. In this study, we compare several hybrid algorithms for optimizing an offshore jacket substructure (JSS). Moreover, we propose a novel hybrid algorithm called the divisional model genetic algorithm (DMGA) to improve efficiency. By adding different methods, namely particle swarm optimization (PSO), pattern search (PS) and targeted mutation (TM) in three subpopulations to become “divisions,” each division has unique functionalities. With the collaboration of these three divisions, this method is considerably more efficient in solving multiple benchmark problems compared with other hybrid algorithms. These results reveal the superiority of DMGA in solving structural optimization problems.

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Kuo, Cheng Chien, Hung Cheng Chen, Teng Fa Taso, and Chin Ming Chiang. "A Modified Particle Swarm Optimization Algorithm with Cases Studies." Advanced Materials Research 268-270 (July 2011): 823–28. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.823.

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s paper presents a hybrid algorithm, the “particle swarm optimization with simulated annealing behavior (SA-PSO)” algorithm, which combines the advantages of good solution quality in simulated annealing and fast calculation in particle swarm optimization. As stochastic optimization algorithms are sensitive to its parameters, this paper introduces criteria in selecting parameters to improve solution quality. To prove the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimized functions of different dimensions. The results made from different algorithms are then compared between the quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the simulation results, SA-PSO obtained higher efficiency, better quality and faster convergence speed than other compared algorithms.

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D’Agostino, Daniele, Giulia Pasquale, Andrea Clematis, et al. "Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems." BioMed Research International 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/980501.

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There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC) simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.

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Yiou, Pascal, and Aglaé Jézéquel. "Simulation of extreme heat waves with empirical importance sampling." Geoscientific Model Development 13, no. 2 (2020): 763–81. http://dx.doi.org/10.5194/gmd-13-763-2020.

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Abstract. Simulating ensembles of extreme events is a necessary task to evaluate their probability distribution and analyze their meteorological properties. Algorithms of importance sampling have provided a way to simulate trajectories of dynamical systems (like climate models) that yield extreme behavior, like heat waves. Such algorithms also give access to the return periods of such events. We present an adaptation based on circulation analogues of importance sampling to provide a data-based algorithm that simulates extreme events like heat waves in a realistic way. This algorithm is a modification of a stochastic weather generator, which gives more weight to trajectories with higher temperatures. This presentation outlines the methodology using European heat waves and illustrates the spatial and temporal properties of simulations.

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Yu, Hang, Yu Zhang, Pengxing Cai, Junyan Yi, Sheng Li, and Shi Wang. "Stochastic Multiple Chaotic Local Search-Incorporated Gradient-Based Optimizer." Discrete Dynamics in Nature and Society 2021 (December 2, 2021): 1–16. http://dx.doi.org/10.1155/2021/3353926.

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In this study, a hybrid metaheuristic algorithm chaotic gradient-based optimizer (CGBO) is proposed. The gradient-based optimizer (GBO) is a novel metaheuristic inspired by Newton’s method which has two search strategies to ensure excellent performance. One is the gradient search rule (GSR), and the other is local escaping operation (LEO). GSR utilizes the gradient method to enhance ability of exploitation and convergence rate, and LEO employs random operators to escape the local optima. It is verified that gradient-based metaheuristic algorithms have obvious shortcomings in exploration. Meanwhile, chaotic local search (CLS) is an efficient search strategy with randomicity and ergodicity, which is usually used to improve global optimization algorithms. Accordingly, we incorporate GBO with CLS to strengthen the ability of exploration and keep high-level population diversity for original GBO. In this study, CGBO is tested with over 30 CEC2017 benchmark functions and a parameter optimization problem of the dendritic neuron model (DNM). Experimental results indicate that CGBO performs better than other state-of-the-art algorithms in terms of effectiveness and robustness.

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Ben Halima Abid, Donia, Saif Eddine Abouda, Hanane Medhaffar, and Mohamed Chtourou. "An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques." Complexity 2021 (August 20, 2021): 1–29. http://dx.doi.org/10.1155/2021/8525090.

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This paper proposes an innovative identification approach of nonlinear stochastic systems using Hammerstein–Wiener (HW) model with output-error autoregressive (OEA) noise. Two fuzzy systems are suggested for the identification of the input and output nonlinear blocks of a proposed model from given input-output data measurements. In this work, the need for the commonly used assumptions including well-known structure of input and/or output nonlinearities and/or reversible nonlinear output is eliminated by replacing the intermediate variables and noise with their estimates. Four parametric estimation algorithms to identify the proposed fuzzy-type stochastic output-error autoregressive HW (FSOEAHW) model are derived based on backpropagation algorithm and multi-innovation and data filtering identification techniques. The proposed algorithms are improved backpropagation gradient (IBPG) algorithm, multi-innovation IBPG (MIIBPG) algorithm, a data filtering IBPG (FIBPG) algorithm, and a multi-innovation-based FIBPG (MIFIBPG) algorithm. The convergence of the parameter estimation algorithms is studied. The effectiveness of the proposed algorithms is shown by a given simulation example.

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Koerkamp, Bas Groot, Theo Stijnen, Milton C. Weinstein, and M. G. Myriam Hunink. "The Combined Analysis of Uncertainty and Patient Heterogeneity in Medical Decision Models." Medical Decision Making 31, no. 4 (2010): 650–61. http://dx.doi.org/10.1177/0272989x10381282.

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The analysis of both patient heterogeneity and parameter uncertainty in decision models is increasingly recommended. In addition, the complexity of current medical decision models commonly requires simulating individual subjects, which introduces stochastic uncertainty. The combined analysis of uncertainty and heterogeneity often involves complex nested Monte Carlo simulations to obtain the model outcomes of interest. In this article, the authors distinguish eight model types, each dealing with a different combination of patient heterogeneity, parameter uncertainty, and stochastic uncertainty. The analyses that are required to obtain the model outcomes are expressed in equations, explained in stepwise algorithms, and demonstrated in examples. Patient heterogeneity is represented by frequency distributions and analyzed with Monte Carlo simulation. Parameter uncertainty is represented by probability distributions and analyzed with 2nd-order Monte Carlo simulation (aka probabilistic sensitivity analysis). Stochastic uncertainty is analyzed with 1st-order Monte Carlo simulation (i.e., trials or random walks). This article can be used as a reference for analyzing complex models with more than one type of uncertainty and patient heterogeneity.

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Karimi, Mohammad, Maryam Miriestahbanati, Hamed Esmaeeli, and Ciprian Alecsandru. "Multi-Objective Stochastic Optimization Algorithms to Calibrate Microsimulation Models." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 4 (2019): 743–52. http://dx.doi.org/10.1177/0361198119838260.

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The calibration process for microscopic models can be automatically undertaken using optimization algorithms. Because of the random nature of this problem, the corresponding objectives are not simple concave functions. Accordingly, such problems cannot easily be solved unless a stochastic optimization algorithm is used. In this study, two different objectives are proposed such that the simulation model reproduces real-world traffic more accurately, both in relation to longitudinal and lateral movements. When several objectives are defined for an optimization problem, one solution method may aggregate the objectives into a single-objective function by assigning weighting coefficients to each objective before running the algorithm (also known as an a priori method). However, this method does not capture the information exchange among the solutions during the calibration process, and may fail to minimize all the objectives at the same time. To address this limitation, an a posteriori method (multi-objective particle swarm optimization, MOPSO) is employed to calibrate a microscopic simulation model in one single step while minimizing the objectives functions simultaneously. A set of traffic data collected by video surveillance is used to simulate a real-world highway in VISSIM. The performance of the a posteriori-based MOPSO in the calibration process is compared with a priori-based optimization methods such as particle swarm optimization, genetic algorithm, and whale optimization algorithm. The optimization methodologies are implemented in MATLAB and connected to VISSIM using its COM interface. Based on the validation results, the a posteriori-based MOPSO leads to the most accurate solutions among the tested algorithms with respect to both objectives.

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Mongwe, Wilson Tsakane, Rendani Mbuvha, and Tshilidzi Marwala. "Locally Scaled and Stochastic Volatility Metropolis– Hastings Algorithms." Algorithms 14, no. 12 (2021): 351. http://dx.doi.org/10.3390/a14120351.

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Markov chain Monte Carlo (MCMC) techniques are usually used to infer model parameters when closed-form inference is not feasible, with one of the simplest MCMC methods being the random walk Metropolis–Hastings (MH) algorithm. The MH algorithm suffers from random walk behaviour, which results in inefficient exploration of the target posterior distribution. This method has been improved upon, with algorithms such as Metropolis Adjusted Langevin Monte Carlo (MALA) and Hamiltonian Monte Carlo being examples of popular modifications to MH. In this work, we revisit the MH algorithm to reduce the autocorrelations in the generated samples without adding significant computational time. We present the: (1) Stochastic Volatility Metropolis–Hastings (SVMH) algorithm, which is based on using a random scaling matrix in the MH algorithm, and (2) Locally Scaled Metropolis–Hastings (LSMH) algorithm, in which the scaled matrix depends on the local geometry of the target distribution. For both these algorithms, the proposal distribution is still Gaussian centred at the current state. The empirical results show that these minor additions to the MH algorithm significantly improve the effective sample rates and predictive performance over the vanilla MH method. The SVMH algorithm produces similar effective sample sizes to the LSMH method, with SVMH outperforming LSMH on an execution time normalised effective sample size basis. The performance of the proposed methods is also compared to the MALA and the current state-of-art method being the No-U-Turn sampler (NUTS). The analysis is performed using a simulation study based on Neal’s funnel and multivariate Gaussian distributions and using real world data modeled using jump diffusion processes and Bayesian logistic regression. Although both MALA and NUTS outperform the proposed algorithms on an effective sample size basis, the SVMH algorithm has similar or better predictive performance when compared to MALA and NUTS across the various targets. In addition, the SVMH algorithm outperforms the other MCMC algorithms on a normalised effective sample size basis on the jump diffusion processes datasets. These results indicate the overall usefulness of the proposed algorithms.

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Mohamed, Linah, Mike Christie, and Vasily Demyanov. "Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification." SPE Journal 15, no. 01 (2009): 31–38. http://dx.doi.org/10.2118/119139-pa.

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Summary History matching and uncertainty quantification are two important research topics in reservoir simulation currently. In the Bayesian approach, we start with prior information about a reservoir (e.g., from analog outcrop data) and update our reservoir models with observations (e.g., from production data or time-lapse seismic). The goal of this activity is often to generate multiple models that match the history and use the models to quantify uncertainties in predictions of reservoir performance. A critical aspect of generating multiple history-matched models is the sampling algorithm used to generate the models. Algorithms that have been studied include gradient methods, genetic algorithms, and the ensemble Kalman filter (EnKF). This paper investigates the efficiency of three stochastic sampling algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm Optimization (PSO) algorithm, and the Neighbourhood Algorithm (NA). HMC is a Markov chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to achieve larger jumps than are possible with other MCMC techniques. PSO is a swarm intelligence algorithm that uses similar dynamics to HMC to guide the search but incorporates acceleration and damping parameters to provide rapid convergence to possible multiple minima. NA is a sampling technique that uses the properties of Voronoi cells in high dimensions to achieve multiple history-matched models. The algorithms are compared by generating multiple history- matched reservoir models and comparing the Bayesian credible intervals (p10-p50-p90) produced by each algorithm. We show that all the algorithms are able to find equivalent match qualities for this example but that some algorithms are able to find good fitting models quickly, whereas others are able to find a more diverse set of models in parameter space. The effects of the different sampling of model parameter space are compared in terms of the p10-p50-p90 uncertainty envelopes in forecast oil rate. These results show that algorithms based on Hamiltonian dynamics and swarm intelligence concepts have the potential to be effective tools in uncertainty quantification in the oil industry.

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Barrera, Antonio, Patricia Román-Román, and Francisco Torres-Ruiz. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms." Mathematics 9, no. 9 (2021): 959. http://dx.doi.org/10.3390/math9090959.

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The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

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Li, H., Y. Cao, L. R. Petzold, and D. T. Gillespie. "Algorithms and Software for Stochastic Simulation of Biochemical Reacting Systems." Biotechnology Progress 24, no. 1 (2008): 56–61. http://dx.doi.org/10.1021/bp070255h.

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Ghosh, Debraj, and Rajat K. De. "Slow update stochastic simulation algorithms for modeling complex biochemical networks." Biosystems 162 (December 2017): 135–46. http://dx.doi.org/10.1016/j.biosystems.2017.10.011.

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Peyton Jones, James C., Jesse Frey, and Saeed Shayestehmanesh. "Stochastic Simulation and Performance Analysis of Classical Knock Control Algorithms." IEEE Transactions on Control Systems Technology 25, no. 4 (2017): 1307–17. http://dx.doi.org/10.1109/tcst.2016.2603065.

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Bayati, Basil, Philippe Chatelain, and Petros Koumoutsakos. "D-leaping: Accelerating stochastic simulation algorithms for reactions with delays." Journal of Computational Physics 228, no. 16 (2009): 5908–16. http://dx.doi.org/10.1016/j.jcp.2009.05.004.

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Cousins, Steve B., William Chen, and Mark E. Frisse. "A tutorial introduction to stochastic simulation algorithms for belief networks." Artificial Intelligence in Medicine 5, no. 4 (1993): 315–40. http://dx.doi.org/10.1016/0933-3657(93)90020-4.

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Zakovryashin, Andrey V., and Sergei M. Prigarin. "Numerical simulation of optical phenomena in atmospheric clouds and fogs." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 6 (2020): 367–75. http://dx.doi.org/10.1515/rnam-2020-0030.

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AbstractWe present algorithms for fast computation of phase functions of atmospheric clouds and for stochastic simulation of such optical phenomena as fogbows, glories, coronas and halos. Using the developed numerical algorithms and software, we analyze optical phenomena for several cloud and fog models.

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Liu, Pai, Xi Zhang, Zhongshun Shi, and Zewen Huang. "Simulation Optimization for MRO Systems Operations." Asia-Pacific Journal of Operational Research 34, no. 02 (2017): 1750003. http://dx.doi.org/10.1142/s0217595917500038.

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In this paper, we address the scheduling issues in a class of maintenance, repair and overhaul systems. By considering all key characteristics such as disassembly, material recovery uncertainty, material matching requirements, stochastic routings and variable processing times, the scheduling problem is formulated into a simulation optimization problem. To solve this difficult problem, we developed two hybrid algorithms based on nested partitions method and optimal computing budged allocation technology. Asymptotic convergence of these two algorithms is proved and numerical results show that the proposed algorithms can generate high quality solutions which outperform the performance of many heuristics.

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Chen, Haihua, Shibao Li, Jianhang Liu, Yiqing Zhou, and Masakiyo Suzuki. "Efficient AM Algorithms for Stochastic ML Estimation of DOA." International Journal of Antennas and Propagation 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/4926496.

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The estimation of direction-of-arrival (DOA) of signals is a basic and important problem in sensor array signal processing. To solve this problem, many algorithms have been proposed, among which the Stochastic Maximum Likelihood (SML) is one of the most concerned algorithms because of its high accuracy of DOA. However, the estimation of SML generally involves the multidimensional nonlinear optimization problem. As a result, its computational complexity is rather high. This paper addresses the issue of reducing computational complexity of SML estimation of DOA based on the Alternating Minimization (AM) algorithm. We have the following two contributions. First using transformation of matrix and properties of spatial projection, we propose an efficient AM (EAM) algorithm by dividing the SML criterion into two components. One depends on a single variable parameter while the other does not. Second when the array is a uniform linear array, we get the irreducible form of the EAM criterion (IAM) using polynomial forms. Simulation results show that both EAM and IAM can reduce the computational complexity of SML estimation greatly, while IAM is the best. Another advantage of IAM is that this algorithm can avoid the numerical instability problem which may happen in AM and EAM algorithms when more than one parameter converges to an identical value.

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Barone, Piero, and Arnolodo Frigessi. "Improving Stochastic Relaxation for Gussian Random Fields." Probability in the Engineering and Informational Sciences 4, no. 3 (1990): 369–89. http://dx.doi.org/10.1017/s0269964800001674.

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In this paper, we are concerned with the simulation of Gaussian random fields by means of iterative stochastic algorithms, which are compared in terms of rate of convergence. A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established. A suitable choice for the parameter improves the rate of convergence with respect to stochastic relaxation for special classes of covariance matrices. Some examples and numerical experiments are given.

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CHAI, RUISHUAI. "FRACTAL DIMENSION OF FRACTIONAL BROWNIAN MOTION BASED ON RANDOM SETS." Fractals 28, no. 08 (2020): 2040020. http://dx.doi.org/10.1142/s0218348x20400204.

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The fractal dimension of fractional Brownian motion can effectively describe random sets, reflecting the regularity implicit in complex random sets. Data mining algorithms based on fractal theory usually follow the calculation of the fractal dimension of fractional Brownian motion. However, the existing fractal dimension calculation methods of fractal Brownian motion have high time complexity and space complexity, which greatly reduces the efficiency of the algorithm and makes it difficult for the algorithm to adapt to high-speed and massive data flow environments. Therefore, several existing fractal dimension calculation methods of fractional Brownian motion are summarized and analyzed, and a random method is proposed, which uses a fixed memory space to quickly estimate the associated dimension of the data stream. Finally, a comparison experiment with existing algorithms proves the effectiveness of this random algorithm. Second, in the sense of two different measures, based on the principle of stochastic comparison, the stability of the stochastic fuzzy differential equations is derived using the stability of the comparison equations, and the practical stability criterion of two measures according to probability is obtained. Then, the stochastic fuzzy differential equations are discussed. The definition of stochastic exponential stability is given and the stochastic exponential stability criterion is proved.

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Merheb, Abdel-Razzak, Hassan Noura, and François Bateman. "Mathematical Modeling of Ecological Systems Algorithm." Lebanese Science Journal 22, no. 2 (2022): 209–31. http://dx.doi.org/10.22453/lsj-022.2.209-231.

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In this paper, the mathematical modeling of a new bio-inspired evolutionary search algorithm called Ecological Systems Algorithm (ESA) is presented. ESA imitates ecological rules to find iteratively the optimum of a given function through interaction between predator and prey search species. ESA is then compared to the well-known Genetic Algorithm which is a powerful bio-inspired stochastic search/optimization algorithm used for decades. Simulation results of the two algorithms optimizing ten different benchmark functions are used to investigate and compare both algorithms based on their speed, performance, reliability, and efficiency.

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Zhang, Yanhui, and Wenyu Yang. "A comparative study of the stochastic simulation methods applied in structural health monitoring." Engineering Computations 31, no. 7 (2014): 1484–513. http://dx.doi.org/10.1108/ec-07-2013-0185.

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Purpose – The purpose of this paper is to discuss the characteristics of several stochastic simulation methods applied in computation issue of structure health monitoring (SHM). Design/methodology/approach – On the basis of the previous studies, this research focusses on four promising methods: transitional Markov chain Monte Carlo (TMCMC), slice sampling, slice-Metropolis-Hasting (M-H), and TMCMC-slice algorithm. The slice-M-H is the improved slice sampling algorithm, and the TMCMC-slice is the improved TMCMC algorithm. The performances of the parameters samples generated by these four algorithms are evaluated using two examples: one is the numerical example of a cantilever plate; another is the plate experiment simulating one part of the mechanical structure. Findings – Both the numerical example and experiment show that, identification accuracy of slice-M-H is higher than that of slice sampling; and the identification accuracy of TMCMC-slice is higher than that of TMCMC. In general, the identification accuracy of the methods based on slice (slice sampling and slice-M-H) is higher than that of the methods based on TMCMC (TMCMC and TMCMC-slice). Originality/value – The stochastic simulation methods evaluated in this paper are mainly two categories of representative methods: one introduces the intermediate probability density functions, and another one is the auxiliary variable approach. This paper provides important references about the stochastic simulation methods to solve the ill-conditioned computation issue, which is commonly encountered in SHM.

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Mikhailov, Guennady A., and Ilia N. Medvedev. "New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 4 (2021): 219–25. http://dx.doi.org/10.1515/rnam-2021-0018.

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Abstract Correlative randomized algorithms are constructed by simple randomization of the algorithm of maximum cross-section (equalization, delta tracking) with the use of a one-dimensional distribution and the correlation function or only correlation length of a random medium. The value of the used correlation length can be adjusted using simple test studies. The calculations carried out confirmed the practical effectiveness of the new algorithms.

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Mikhailov, Guennady A., and Ilia N. Medvedev. "New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 4 (2021): 219–25. http://dx.doi.org/10.1515/rnam-2021-0018.

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Abstract Correlative randomized algorithms are constructed by simple randomization of the algorithm of maximum cross-section (equalization, delta tracking) with the use of a one-dimensional distribution and the correlation function or only correlation length of a random medium. The value of the used correlation length can be adjusted using simple test studies. The calculations carried out confirmed the practical effectiveness of the new algorithms.

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Warne, David J., Ruth E. Baker, and Matthew J. Simpson. "Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art." Journal of The Royal Society Interface 16, no. 151 (2019): 20180943. http://dx.doi.org/10.1098/rsif.2018.0943.

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Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab ® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

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Ma, Yimin, and Shuli Sun. "Distributed Optimal and Self-Tuning Filters Based on Compressed Data for Networked Stochastic Uncertain Systems with Deception Attacks." Sensors 23, no. 1 (2022): 335. http://dx.doi.org/10.3390/s23010335.

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In this study, distributed security estimation problems for networked stochastic uncertain systems subject to stochastic deception attacks are investigated. In sensor networks, the measurement data of sensor nodes may be attacked maliciously in the process of data exchange between sensors. When the attack rates and noise variances for the stochastic deception attack signals are known, many measurement data received from neighbour nodes are compressed by a weighted measurement fusion algorithm based on the least-squares method at each sensor node. A distributed optimal filter in the linear minimum variance criterion is presented based on compressed measurement data. It has the same estimation accuracy as and lower computational cost than that based on uncompressed measurement data. When the attack rates and noise variances of the stochastic deception attack signals are unknown, a correlation function method is employed to identify them. Then, a distributed self-tuning filter is obtained by substituting the identified results into the distributed optimal filtering algorithm. The convergence of the presented algorithms is analyzed. A simulation example verifies the effectiveness of the proposed algorithms.

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Dingemanse, Gertjan, and André Goedegebure. "Efficient Adaptive Speech Reception Threshold Measurements Using Stochastic Approximation Algorithms." Trends in Hearing 23 (January 2019): 233121652091919. http://dx.doi.org/10.1177/2331216520919199.

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This study examines whether speech-in-noise tests that use adaptive procedures to assess a speech reception threshold in noise ( SRT50n) can be optimized using stochastic approximation (SA) methods, especially in cochlear-implant (CI) users. A simulation model was developed that simulates intelligibility scores for words from sentences in noise for both CI users and normal-hearing (NH) listeners. The model was used in Monte Carlo simulations. Four different SA algorithms were optimized for use in both groups and compared with clinically used adaptive procedures. The simulation model proved to be valid, as its results agreed very well with existing experimental data. The four optimized SA algorithms all provided an efficient estimation of the SRT50n. They were equally accurate and produced smaller standard deviations (SDs) than the clinical procedures. In CI users, SRT50n estimates had a small bias and larger SDs than in NH listeners. At least 20 sentences per condition and an initial signal-to-noise ratio below the real SRT50n were required to ensure sufficient reliability. In CI users, bias and SD became unacceptably large for a maximum speech intelligibility score in quiet below 70%. In conclusion, SA algorithms with word scoring in adaptive speech-in-noise tests are applicable to various listeners, from CI users to NH listeners. In CI users, they lead to efficient estimation of the SRT50n as long as speech intelligibility in quiet is greater than 70%. SA procedures can be considered as a valid, more efficient, and alternative to clinical adaptive procedures currently used in CI users.

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Nikolic, Kostantin. "Training Neural Network Elements Created From Long Shot Term Memory." Oriental journal of computer science and technology 10, no. 1 (2017): 01–10. http://dx.doi.org/10.13005/ojcst/10.01.01.

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This paper presents the application of stochastic search algorithms to train artificial neural networks. Methodology approaches in the work created primarily to provide training complex recurrent neural networks. It is known that training recurrent networks is more complex than the type of training feedforward neural networks. Through simulation of recurrent networks is realized propagation signal from input to output and training process achieves a stochastic search in the space of parameters. The performance of this type of algorithm is superior to most of the training algorithms, which are based on the concept of gradient. The efficiency of these algorithms is demonstrated in the training network created from units that are characterized by long term and long shot term memory of networks. The presented methology is effective and relative simple.

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Ha, Seung-Yeal, Myeongju Kang, Dohyun Kim, Jeongho Kim, and Insoon Yang. "Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence." Mathematical Models and Methods in Applied Sciences 32, no. 03 (2022): 533–617. http://dx.doi.org/10.1142/s0218202522500130.

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We study a consensus-based method for minimizing a nonconvex function over the Stiefel manifold. The consensus dynamics consists of stochastic differential equations for interacting particle system, whose trajectory is guaranteed to stay on the Stiefel manifold. For the proposed model, we prove the mean-field limit of the stochastic system toward a nonlinear Fokker–Planck equation on the Stiefel manifold. Moreover, we provide a sufficient condition on the parameter and the initial data, so that the solution to the Fokker–Planck equation is asymptotically concentrated on the point near a global optimizer. To implement our consensus-based optimization (CBO) algorithm, we provide two algorithms; one is improved from the algorithm suggested in our previous work, and the other is based on an entirely different approach, namely the Cayley transformation. We validate the CBO algorithms on the various test problems on the Stiefel manifold.

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