CAREER: Reaction-Diffusion Kinetics with Tensor Networks

在西北大学化学系化学理论、模型和计算方法项目的支持下，托德·金里奇将开发和评估模拟反应扩散动力学的算法。生物和合成系统中的许多自组装和信号转导过程都是通过分子的反应和扩散来实现的。例如，蛋白质在信号级联中相互勾结，以检测刺激并将该检测转化为所需的反应。虽然在理解自然系统和工程合成系统方面都取得了很大进展，但化学反应网络（CRN）仍然构成挑战，特别是在考虑分子尺度的随机波动特征时。 目前，重复的噪声模拟可以结合起来，以评估如何快速的时间尺度事件（个人反应和扩散步骤）建立在一起，以产生慢时间尺度的反应。Gingrich博士和他的研究小组将利用一种称为张量网络（TN）的数学结构来追求计算方法，这些方法可以产生新的方法来分析CRN，而无需多次重复模拟。这项工作将导致传播的计算机代码，这也将形成两个基于网络的教育模拟模块的基础上波动的化学动力学。连接微观相互作用与新兴的宏观现象是统计力学的核心挑战。在化学动力学中，这一挑战表现在非平衡时空模式中，这种模式来自化学反应和扩散之间的平衡。CRN中物种之间动力学相互作用的微妙变化可以敏感地影响出现的模式，例如，振荡化学钟、图灵模式和细胞信号转导。Gingrich团队将开发、表征、优化并最终应用一种新的计算方法来研究模式对微观动力学模型的敏感性。该研究计划将结合联合收割机分析技术被称为土井Peliti（DP）框架与成熟的计算方法TN多体问题，提供一个替代的角度来解决动力学问题，这是经常攻击通过蒙特卡洛采样单独。一个附带的教育计划将使用网络模拟来教授随机动力学的各个方面，其中一个模块针对本科生，另一个模块针对研究生。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the Chemical Theory, Models, and Computational Methods Program in the Division of Chemistry Todd Gingrich of Northwestern University will develop and assess algorithms for simulating reaction-diffusion kinetics. Many self-assembly and signal transduction processes in both biological and synthetic systems are implemented through the reaction and diffusion of molecules. For example, proteins collude together in signaling cascades to detect stimuli and transduce that detection into a desired response. While there has been great progress both in understanding natural systems and in engineering synthetic ones, chemical reaction networks (CRNs) continue to pose a challenge, particularly when accounting for random fluctuations characteristic to the molecular scale. Currently, repeated noisy simulations can be combined to assess how fast-timescale events (individual reactions and diffusive steps) build together to generate slow-timescale responses. Dr. Gingrich and his research group will utilize a mathematical construction called a tensor network (TN) to pursue computational approaches that yield novel methods to analyze CRNs without the need for many repeated simulations. The work will result in disseminated computer code, which will also form the basis for two educational web-based simulation modules about fluctuations in chemical kinetics.Connecting microscopic interactions with emergent macroscopic phenomena is a central challenge of statistical mechanics. In chemical kinetics, this challenge manifests in the nonequilibrium spatio-temporal patterns which emerge from a balance between chemical reactions and diffusion. Subtle changes in the kinetic interactions between species in CRNs can sensitively impact the patterns that emerge, e.g., oscillatory chemical clocks, Turing patterns, and cellular signal transduction. The Gingrich team will develop, characterize, optimize, and ultimately apply a new computational method to study the sensitivity of patterns to the microscopic kinetic model. The research program will combine analytical techniques known as the Doi-Peliti (DP) framework with mature computational methods for TN many-body problems to offer an alternative perspective to kinetics problems which are routinely attacked through Monte Carlo sampling alone. An accompanying educational plan will use web simulations to teach aspects of stochastic kinetics, with one module targeting undergraduates and another targeting graduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.