Using Mixed Discrete-Continuum Representations to Characterize the Dynamics of Large Many-Body Dynamics Problems

这个项目的目标是了解如何使用计算机模拟来预测通过摩擦和接触相互作用的物体大系统的运动。研究这些所谓的“多体动力学问题”在多个学科(物理、化学、天文学、地质力学)、工业(制药、食品加工、农业、制造、建筑、采矿)和工程应用(添加剂制造、纳米粒子自组装、机器人、地面车辆移动性)中具有理论和实践意义。在教育和外联影响方面，作为该项目的一部分采取的举措将：(1)分别通过“视频游戏背后的科学”短期课程和居民暑期方案，在初中和高中促进计算科学学科；(2)更新和扩大关于高性能计算和高级计算动力学的两门研究生课程的课程；(3)扩大一年两次的促进技术转让的高级计算论坛；以及，(Iv)通过工程硕士远程学习计划为需要分析、处理和解决问题的从业者提供培训，这些从业者需要使用工程设计和工业操作中越来越多的数据收集产生的信息来分析、处理和解决问题。研究工作将集中在研究在多体动力学问题的模拟中促进离散-连续双重表示的技术。回答的基本问题是，人们应该如何使用连续统形式来处理多体动力学问题的部分内容，以便新的离散-连续统混合表示法设法保持原始问题的动力学？此外，应该如何将连续表示细化为离散表示，反之，应该使用什么技术将离散表示粗粒度表示为连续表示？机械工程专业知识(多体系统动力学、固体力学、塑性学)、应用数学技术(求解偏微分方程的无网格法、最优化方法)和计算机科学组件(机器学习、软件工程)将结合在一起，共同解决所述问题。在这方面，本项目的目标是：(A)建立一种产生流变学的系统方法，当这种方法嵌入连续介质力学模型时，产生一个接近于大型离散多体动力学问题的解；以及(B)使用这一方法来了解是否存在具有普遍属性的流变学；即，适用于所有或大范围多体动力学问题的流变学。在这种情况下，流变学被认为是一种在微观尺度上将连续统的动力学/流动与作用在其上的力联系起来的方法论。这项研究计划是围绕着通过机器学习过程增强物理洞察力的想法建立的，机器学习过程使用完全解析的多体动力学解决方案生成的大量数据来产生流变学候选对象。

The goal of this project is to understand how computer simulation can be used to predict the motion of large systems of bodies interacting with each other through friction and contact. Studying these so-called "many-body dynamics problems" has theoretical and practical relevance in several disciplines (physics, chemistry, astronomy, geomechanics), industries (pharmaceuticals, food processing, farming, manufacturing, construction, mining), and engineering applications (additive manufacturing, nanoparticle self-assembly, robotics, ground vehicle mobility). In terms of educational and outreach impact, initiatives undertaken as part of this project will (i) promote the discipline of Computational Science at middle and high-school levels via a "The Science Behind Video Gaming" short course and a residential summer program, respectively; (ii) update and expand curricula in two graduate courses on high performance computing and advanced computational dynamics; (iii) expand a biannual advanced computing forum that facilitates transfer of technology; and, (iv) provide training via a Master of Engineering distance learning program for practitioners who need to analyze, process, and solve problems using information generated by the growing use of data collection in engineering design and industrial operations.The research effort will focus on investigating techniques that facilitate a discrete-continuum dual representation in the simulation of many-body dynamics problems. The fundamental question answered is how should one handle parts of a many-body dynamics problem using a continuum formalism so that the new mixed discrete-continuum representation manages to preserve the dynamics of the original problem? Also, how should a continuum representation be fine-grained into a discrete one, and conversely, what techniques should be used to coarse-grain a discrete representation into a continuous one? Mechanical engineering expertise (dynamics of many-body systems, solid mechanics, plasticity), applied math techniques (meshless methods for solving partial differential equations, optimization methods), and computer science components (machine learning, software engineering) will combine in a coordinated effort to solve the stated problem. In this context, the goal of this project is to (a) establish a systematic methodology for producing rheologies that, when embedded in a continuum mechanics model, produce a solution that is close to that of a large discrete many-body dynamics problem; and (b) use this methodology to understand whether there are rheologies that have a universal attribute; i.e., that are applicable to all, or a large spectrum of, many-body dynamics problems. In this context, a rheology is regarded as a methodology that ties at microscale the dynamics/flow of a continuum to the forces acting on it. The research plan is built around the idea of augmenting physical insights with a machine learning process that uses large amounts of data generated by fully-resolved, many-body dynamics solutions to produce rheology candidates.