从基于个体的生物扩散模型中提取种群水平行为的无方程计算方法
An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
摘要：
许多生物体的运动可以被描述为在个体和群体水平上的随机行走。这种随机游走的规则是基于复杂的生物过程，可能很难开发出一个易于处理的、定量准确的、个体水平的模型。然而，从生态学到医学等领域的重要问题涉及大量的个体，进一步的智力挑战是基于详细的个体水平模型来建模群体水平的行为。由于大量的相互作用的个体，因为个体层次的模型是复杂的，经典的直接蒙特卡罗模拟可以是非常缓慢的，往往很少有实际用途。在这种情况下，一个方程的自由的方法可以提供有效的方法来分析和模拟的个人为基础的模型。本文分析了无方程粗射影积分。为了分析的目的，我们开始与已知的偏微分方程描述生物随机游动，我们研究这些方程的投影积分。特别是，我们说明了如何加快显式数值方法求解这些方程。然后，我们提出了说明性的动力学蒙特卡罗模拟这些随机游走，并显示减少计算时间多达一千的因素，可以通过利用封闭形式的偏微分方程的分析开发的想法。这里的生物学例子是趋化性，但它可以是任何随机步行者，它会根据环境线索来调整自己的运动。
英文摘要：
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging from ecology to medicine involve large collections of individuals, and a further intellectual challenge is to model population-level behavior based on a detailed individual-level model. Because of the large number of interacting individuals and because the individual-level model is complex, classical direct Monte Carlo simulations can be very slow, and often of little practical use. In this case, an equation-free approach may provide effective methods for the analysis and simulation of individual-based models. In this paper we analyze equation-free coarse projective integration. For analytical purposes, we start with known partial differential equations describing biological random walks and we study the projective integration of these equations. In particular, we illustrate how to accelerate explicit numerical methods for solving these equations. Then we present illustrative kinetic Monte Carlo simulations of these random walks and show a decrease in computational time by as much as a factor of a thousand can be obtained by exploiting the ideas developed by analysis of the closed form PDEs. The illustrative biological example here is chemotaxis, but it could be any random walker which biases its movement in response to environmental cues.
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