Big Data for Fast and Accurate Numerical Simulation of Mechanical Structures

大数据用于快速准确的机械结构数值模拟

• 批准号: RGPIN-2017-05524
• 负责人: Levin, David
• 金额: $ 2.04万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711682
• 关键词: Big; Data; Fast; Accurate; Numerical

Numerical simulations of physical phenomena such as large and small deformations are a crucial tool for everything from building design to 3D printing. The knowledge of how something will perform in the real-world has a tremendous impact on the design process. However, even today, state-of-the-art algorithms are still several orders of magnitude too slow to be used interactively, especially when we consider constraints imposed by desired accuracy and computational challenges introduced by the high-resolution, multi-material nature of advanced additive manufacturing techniques. The problem becomes more daunting when one considers that next-generation interactive design tools for buildings, airplanes, cars and even characters in blockbuster films desire "in-the-loop" simulation. Such a setup has two principal benefits; first, designers can receive feedback on the effect of design changes instantaneously and second, ultra-fast simulation opens the door to intelligent, optimization-based suggestion schemes -- ones which can perform background exploration of the design space in order to find non-intuitive designs which satisfy designer constraints. Currently, numerical simulations are treated as disposable, thrown away once the desired structural analysis or animation has been completed. But why should this be the case ? What could we do with a large database of simulation data? Could we use it to accelerate a broad range of simulations without requiring the tedious and expensive precomputation on a case-by-case basis? In this research project I will explore the implications of this question and develop simulation algorithms which use prior information extracted from such a database to avoid the performance/fidelity trade-offs of traditional methods. Such algorithms could have a plethora of benefits for any domain in which physical simulation is used. In order to do this I will focus on three main areas 1.) Compact, geometry independent representations for storing simulation data 2.) Using stored data for fast, runtime numerical coarsening 3.) Algorithms and devices with which to quickly and accurately capture material and geometry parameters necessary for simulation 4.) New algorithms for solving coupled systems of linear and nonlinear equations which exploit both of the above. Accomplishing these four goals will push us towards a new era of high-performance physics simulations driven by Big Data. Just as how online databases have revolutionized areas such as computer vision, I envision a similar change will occur in the numerical physics and computer animation communities. I believe that this work, essentially building the google image search for simulation data, is crucial for bringing this to fruition.

对大变形和小变形等物理现象的数值模拟是从建筑设计到 3D 打印等各个领域的重要工具。了解事物在现实世界中的表现对设计过程有着巨大的影响。然而，即使在今天，最先进的算法仍然慢了几个数量级，无法交互使用，特别是当我们考虑到所需精度所带来的限制以及先进增材制造技术的高分辨率、多材料特性带来的计算挑战时。 当人们考虑到用于建筑物、飞机、汽车甚至大片中的角色的下一代交互式设计工具都需要“循环内”模拟时，这个问题就变得更加令人畏惧。这种设置有两个主要好处：首先，设计人员可以立即收到有关设计变更效果的反馈，其次，超快速模拟为智能、基于优化的建议方案打开了大门——这些方案可以对设计空间进行背景探索，以找到满足设计人员约束的非直观设计。 目前，数值模拟被视为一次性的，一旦完成所需的结构分析或动画就被丢弃。但为什么会这样呢？我们可以利用大型模拟数据数据库做什么？我们是否可以使用它来加速广泛的模拟，而无需根据具体情况进行繁琐且昂贵的预计算？在这个研究项目中，我将探讨这个问题的含义，并开发模拟算法，该算法使用从此类数据库中提取的先验信息来避免传统方法的性能/保真度权衡。此类算法对于使用物理模拟的任何领域都有很多好处。 为了做到这一点，我将重点关注三个主要领域 1.) 用于存储仿真数据的紧凑、独立于几何形状的表示 2.) 使用存储的数据进行快速、运行时数值粗化 3.) 快速准确地捕获模拟所需的材料和几何参数的算法和设备 4.) 用于求解线性和非线性方程耦合系统的新算法，该算法利用了上述两者。 实现这四个目标将推动我们迈向大数据驱动的高性能物理模拟的新时代。正如在线数据库如何彻底改变计算机视觉等领域一样，我预计数值物理和计算机动画社区也会发生类似的变化。我相信这项工作，本质上是为模拟数据构建谷歌图像搜索，对于实现这一目标至关重要。