CAREER: Particle Methods for High-Dimensional Integro-Differential Simulation with Application to Aerosol Modeling

该学院早期职业发展(CALEAR)计划奖的研究部分旨在开发稳健且可扩展的随机粒子方法来模拟复杂的高维动力系统，其特定的研究目标是实现有效的、粒子分辨的大气气溶胶模型及其气候影响。该研究计划将涉及新的数学技术，使复杂粒子系统的模拟速度大大加快，并使这些方法足够健壮和可靠，足以供工程师和科学家常规使用。研究生和本科生都将参与这项研究，高中年龄的女学生将被邀请参加为期一周的夏令营，以探索动力学和力学方面的想法。除了多样化的学生参与，其他成果将包括新的本科教材，动态模拟的新数学算法，以及高性能粒子模拟的开源代码。这项工作的结果和好处将影响动力系统领域和大气气溶胶模拟的目标应用。通过这项研究增进对气溶胶粒子过程的了解，将有助于更准确地理解气候模拟和气溶胶粒子对人类健康的影响。在更广泛的背景下，该项目是朝着通过计算分析高维复杂动力系统的一般技术迈出的一步，因此有可能为当前的一系列科学挑战做出贡献。研究生和本科生将受益于参与研究和改进课堂教学，而参加夏令营的高中年龄女学生将获得接触和参与工程和科学的机会。

The research component of this Faculty Early Career Development (CAREER) Program award targets the development of robust and scalable stochastic particle methods for simulating complex, high-dimensional dynamical systems, with a particular research goal of enabling efficient, particle-resolved models of atmospheric aerosols and their climate impact. The research program will involve new mathematical techniques to allow dramatically faster simulations of complex particle systems, as well as making the methods robust and reliable enough to be routinely used by engineers and scientists. Students will be involved in the research at both the graduate and undergraduate levels, and high-school-aged female students will be hosted for a week-long summer camp to explore ideas in dynamics and mechanics. In addition to the diverse student involvement, other deliverables will include new undergraduate educational materials, new mathematical algorithms for dynamical simulation, and open-source code for high-performance particle simulation.The outcome and benefits of this work will impact both the areas of dynamical systems and the target application of atmospheric aerosol modeling. The improved understanding of aerosol particle processes generated by this research will contribute to a more accurate understanding of climate modeling and to the impact of aerosol particles on human health. In a broader context, this project is a step towards general techniques for computationally analyzing complex dynamical systems in high dimensions, and thus has the potential to contribute to a wide range of current scientific challenges. Graduate and undergraduate students will benefit from involvement in the research and through improved classroom instruction, while the high-school-aged female students participating in the summer camp will gain exposure and engagement with engineering and science.