MULTISCALE STOCHASTIC REACTION-DIFFUSION ALGORITHMS

多尺度随机反应扩散算法

• 批准号: 1620403
• 负责人: Hye Won Kang
• 金额: $ 20万
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620403&HistoricalAwards=false
• 关键词: MULTISCALE; STOCHASTIC; REACTION; DIFFUSION; ALGORITHMS

Stochastic reaction-diffusion processes are widely used in the modeling of cancer, immune systems, and developmental biology. These processes describe the concentration changes of the chemically reacting species that diffuse through space. Numerical simulation of stochastic reaction-diffusion processes is challenging since the underlying biochemical systems are large in general and naturally involve various scales in the speed of chemical reaction and diffusion and their quantities in different locations. The multiscale nature can slow down the speed of the numerical simulation. Moreover, stochastic simulation requires a set of repeated performance of the simulations to obtain averaged behavior of chemical species. The goal of this project is to develop efficient numerical algorithms for stochastic reaction-diffusion processes by coupling different numerical schemes based on scales and by applying optimal strategies to increase accuracy and efficiency. The ability to simulate large stochastic systems will provide an efficient tool for modeling and understanding of complex biochemical systems. A graduate-level course in the field related to this project will be redesigned. The undergraduate and graduate students will participate in the project and will receive mentorships. This project focuses on the development and the analysis of multiscale numerical algorithms for stochastic reaction-diffusion processes combining different numerical schemes. Markov chain models are widely used to model chemically reacting species with diffusion, but the exact simulation of Markov chain models for large systems are computationally expensive when the systems involve multiscale phenomena. There are many studies to develop and to understand multiscale methods for stochastic reaction-diffusion processes using Markov chain models, but the major drawback in the existing methodologies is that they do not fully account for significant changes in the abundances of chemical species in time and space, which reduce the accuracy of the approximations. In this project, a spatial domain of interest will be divided into several subsets based on the abundance of chemical species and Markov chain models and stochastic partial differential equations will be respectively applied to the different regions. Then, the method will be extended to incorporate moving interfaces between the numerical schemes, which change in time, and to use optimal strategies to find a location of the next reaction. The fast simulation skills of large stochastic reaction-diffusion systems will increase efficiency in the study of experimental science and engineering. Moreover, the results of the proposal will be applied to explore the impact on human development or disease, for example, to find key signaling pathways in cancer or immune systems and to find how the tissues and organs develop to have different functions in the embryo.

随机反应扩散过程广泛应用于癌症、免疫系统和发育生物学的建模。这些过程描述了通过空间扩散的化学反应物质的浓度变化。随机反应扩散过程的数值模拟是具有挑战性的，因为基本的生化系统一般都很大，自然涉及不同尺度的化学反应和扩散的速度及其在不同位置的数量。数值模拟的多尺度性会降低计算速度。此外，随机模拟需要一组重复的模拟性能，以获得平均的化学物种的行为。该项目的目标是通过耦合基于尺度的不同数值方案并通过应用优化策略来提高精度和效率，为随机反应扩散过程开发有效的数值算法。模拟大型随机系统的能力将为复杂生物化学系统的建模和理解提供有效的工具。将重新设计与该项目有关的研究生课程。本科生和研究生将参加该项目，并将获得指导。本计画主要研究结合不同数值模式之随机反应扩散过程之多尺度数值演算法之发展与分析。马尔可夫链模型被广泛用于模拟具有扩散的化学反应物种，但是当系统涉及多尺度现象时，大型系统的马尔可夫链模型的精确模拟在计算上是昂贵的。有许多研究开发和理解多尺度方法的随机反应扩散过程使用马尔可夫链模型，但在现有的方法的主要缺点是，他们没有充分考虑显着变化的化学物种的丰度在时间和空间，这降低了近似的准确性。在本计画中，我们将一个空间区域根据化学物种的丰度分成几个子集，并将马尔可夫链模型和随机偏微分方程分别应用于不同的区域。然后，该方法将被扩展到将移动的界面之间的数值方案，随时间变化，并使用最佳策略来找到下一个反应的位置。大型随机反应扩散系统的快速模拟技术将提高实验科学和工程研究的效率。此外，该提案的结果将用于探索对人类发育或疾病的影响，例如，寻找癌症或免疫系统中的关键信号通路，以及发现组织和器官如何在胚胎中发育为具有不同功能。