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12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation

作者： Randone, Francesca Doz, Romina Cairoli, Francesca Bortolussi, Luca Univ Trieste Trieste Italy

ISBN: (纸本)9783031737084;9783031737091

The probabilistic programming paradigm is gaining popularity due to the possibility of easily representing probabilistic systems and running a number of off-the-shelf inference algorithms on them. This paper explores how this paradigm can be used to analyse collective systems, in the form of Markov Population Processes (MPPs). MPPs have been extensively used to represent systems of interacting agents, but their analysis is challenging due to the high computational cost required to perform exact simulations of the systems. We represent MPPs as runs of the approximate variant of the stochastic simulation algorithm (SSA), known as tau-leaping, which can be seen as a probabilistic program. We apply Gaussian Semantics, a recently proposed inference method for probabilistic programs, to analyse it. We show that tau-leaping runs can be effectively analysed using a tailored version of Second Order Gaussian Approximation in which we use a Gaussian Mixture encoding of Poisson distributions. In the resulting analysis, the state of the system is approximated by a multivariate Gaussian Mixture generalizing other common Gaussian approximations such as the Linear Noise Approximation and the Langevin Method. Preliminary numerical experiments show that this approach is able to analyse MPPs with reasonable accuracy on the significant statistics while avoiding expensive numerical simulations.

关键词： Markov Population Processes stochastic simulation algorithm Probabilistic Programming

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Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach

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EPJ DATA SCIENCE 2018年第1期7卷 24页

作者： Conrad, Natasa Djurdjevac Helfmann, Luzie Zonker, Johannes Winkelmann, Stefanie Schuette, Christof Zuse Inst Berlin Berlin Germany Free Univ Berlin Inst Math & Informat Berlin Germany

Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.

关键词： Agent-based model Diffusion process Spreading process stochastic simulation algorithm Human mobility

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“Final all possible steps”approach for accelerating stochastic simulation of coupled chemical reactions

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Applied Mathematics and Mechanics(English Edition) 2008年第3期29卷 379-387页

作者：周文彭新俊刘祥闫正楼王翼飞 Department of Mathematics Shanghai University

In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂（FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.

关键词： "final all possible steps" approach stochastic simulation algorithm chemically reacting systems

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L-leap:accelerating the stochastic simulation of chemically reacting systems

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Applied Mathematics and Mechanics(English Edition) 2007年第10期28卷 1361-1371页

作者：彭新俊王翼飞 Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.

关键词： L-leap algorithm leap condition stochastic simulation algorithm chemically reacting systems

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Abstract Next Subvolume Method: A logical process-based approach for spatial stochastic simulation of chemical reactions

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2011年第3期35卷 193-198页

作者： Wang, Bing Hou, Bonan Xing, Fei Yao, Yiping Natl Univ Def Technol Sch Comp Sci Changsha 410073 Hunan Peoples R China

The spatial stochastic simulation of biochemical systems requires significant calculation efforts. Parallel discrete-event simulation is a promising approach to accelerate the execution of simulation runs. However, achievable speedup depends on the parallelism inherent in the model. One of our goals is to explore this degree of parallelism in the Next Subvolume Method type simulations. Therefore we introduce the Abstract Next Subvolume Method, in which we decouple the model representation from the sequential simulation algorithms, and prove that state trajectories generated by its executions statistically accord with those generated by the Next Subvolume Method. The experimental performance analysis shows that optimistic synchronization algorithms, together with careful controls over the speculative execution, are necessary to achieve considerable speedup and scalability in parallel spatial stochastic simulation of chemical reactions. Our proposed method facilitates a flexible incorporation of different synchronization algorithms, and can be used to select the proper synchronization algorithm to achieve the efficient parallel simulation of chemical reactions. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： stochastic simulation algorithm Next subvolume Method Spatial stochastic simulation Parallel discrete-event simulation

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Efficient anticorrelated variance reduction for stochastic simulation of biochemical reactions

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IET SYSTEMS BIOLOGY 2019年第1期13卷 16-23页

作者： Vo Hong Thanh Aalto Univ Dept Comp Sci Espoo Finland Univ Trento Microsoft Res Ctr Computat & Syst Biol COSBI Rovereto Trento Italy

We investigate the computational challenge of improving the accuracy of the stochastic simulation estimation by inducing negative correlation through the anticorrelated variance reduction technique. A direct application of the technique to the stochastic simulation algorithm (SSA), employing the inverse transformation, is not efficient for simulating large networks because its computational cost is similar to the sum of independent simulation runs. We propose in this study a new algorithm that employs the propensity bounds of reactions, introduced recently in their rejection-based SSA, to correlate and synchronise the trajectories during the simulation. The selection of reaction firings by our approach is exact due to the rejection-based mechanism. In addition, by applying the anticorrelated variance technique to select reaction firings, our approach can induce substantial correlation between realisations, hence reducing the variance of the estimator. The computational advantage of our rejection-based approach in comparison with the traditional inverse transformation is that it only needs to maintain a single data structure storing propensity bounds of reactions, which is updated infrequently, hence achieving better performance.

关键词： biochemistry data structures biology computing inverse transforms stochastic processes large-scale systems stochastic simulation estimation anticorrelated variance reduction technique stochastic simulation algorithm computational cost independent simulation runs rejection-based SSA reaction firings rejection-based mechanism anticorrelated variance technique substantial correlation estimator rejection-based approach single data structure storing propensity biochemical reactions anticorrelated variance reduction

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ADAPTIVE FINITE ELEMENT METHOD ASSISTED BY stochastic simulation OF CHEMICAL SYSTEMS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2013年第1期35卷 B107-B131页

作者： Cotter, Simon L. Vejchodsky, Tomas Erban, Radek Univ Manchester Sch Math Manchester M13 9PL Lancs England Acad Sci Czech Republ Inst Math CR-11567 Prague 1 Czech Republic Univ Oxford Math Inst Oxford OX1 3LB England

stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods.

关键词： finite element methods chemical Fokker-Planck adaptive meshes stochastic simulation algorithm

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Efficient simulation of discrete stochastic reaction systems with a splitting method

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BIT NUMERICAL MATHEMATICS 2010年第4期50卷 797-822页

作者： Jahnke, Tobias Altintan, Derya Inst Angew & Numer Math Fak Math KIT D-76133 Karlsruhe Germany Middle E Tech Univ Inst Appl Math Dept Comp Sci TR-06531 Ankara Turkey Selcuk Univ Konya Turkey

stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.

关键词： stochastic simulation algorithm Discrete stochastic reaction systems Splitting methods Analytic solution formulas Error bounds Chemical master equation

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From Compositional Petri Net Modeling to Macro and Micro simulation by Means of stochastic simulation and Agent-Based Models

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ACM TRANSACTIONS ON MODELING AND PERFORMANCE EVALUATION OF COMPUTING SYSTEMS 2024年第1期9卷 1-30页

作者： Amparore, Elvio Beccuti, Marco Castagno, Paolo Pernice, Simone Franceschinis, Giuliana Pennisi, Marzio Univ Torino Dipartimento Informat Via Pessinetto 12 I-10149 Turin Italy Univ Piemonte Orientale DiSIT Viale T Michel 11 Alessandria Italy Consorzio Interuniv Nazl Telecomunicazioni UdR UPO Viale T Michel 11 Alessandria Italy

Computational modeling has become a widespread approach for studying real-world phenomena by using different modeling perspectives, in particular, the microscopic point of view concentrates on the behavior of the single components and their interactions from which the global system evolution emerges, while the macroscopic point of view represents the system's overall behavior abstracting as much as possible from that of the single components. The preferred point of view depends on the effort required to develop the model, on the detail level of the available information about the system to be modeled, and on the type of measures that are of interest to the modeler;each point of view may lead to a different modeling language and simulation paradigm. An approach adequate for the microscopic point of view is Agent-Based Modeling and simulation, which has gained popularity in the last few decades but lacks a formal definition common to the different tools supporting it. This may lead to modeling mistakes and wrong interpretation of the results, especially when comparing models of the same system developed according to different points of view. The aim of the work described in this paper is to provide a common compositional modeling language from which both a macro and a micro simulation model can be automatically derived: these models are coherent by construction and may be studied through different simulation approaches and tools. A framework is thus proposed in which a model can be composed using a Petri Net formalism and then studied through both an Agent-Based simulation and a classical stochastic simulation algorithm, depending on the study goal.

关键词： stochastic symmetric nets Agent-Based Models stochastic simulation algorithm

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stochastic simulation of the Cell Cycle Model for Budding Yeast

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Communications in Computational Physics 2011年第2期9卷 390-405页

作者： Di Liu Department of Mathematics Michigan State UniversityEast LansingMI 48824USA

We use the recently proposed Nested stochastic simulation algorithm(Nested SSA)to simulate the cell cycle model for budding *** results show that Nested SSA is able to significantly reduce the computational cost while... 详细信息

关键词： stochastic simulation algorithm stochastic process bio-chemical reacting network system biology

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