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.

物理现象（如大小变形）的数值模拟是从建筑设计到3D打印的一切重要工具。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，最先进的算法仍然太慢了几个数量级，无法交互使用，特别是当我们考虑到高分辨率、多材料的先进增材制造技术所带来的精度限制和计算挑战时。