Big Data for Fast and Accurate Numerical Simulation of Mechanical Structures

物理现象的数值模拟，如大小变形，是从建筑设计到3D打印的重要工具。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和先进增材制造技术的高分辨率、多材料性质所带来的计算挑战所带来的限制时。 当人们考虑到用于建筑物、飞机、汽车甚至是大片中的角色的下一代交互式设计工具需要“在环”仿真时，这个问题变得更加令人生畏。这样的设置有两个主要的好处;第一，设计人员可以即时收到设计更改效果的反馈;第二，超快速模拟为智能的、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，一旦完成了所需的结构分析或动画就被扔掉。但为什么会这样呢？我们可以用一个大型的模拟数据库做什么？我们是否可以使用它来加速广泛的模拟，而不需要在逐个案例的基础上进行繁琐而昂贵的预先计算？在这个研究项目中，我将探讨这个问题的影响，并开发仿真算法，使用从这样的数据库中提取的先验信息，以避免传统方法的性能/保真度权衡。这样的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，我将集中在三个主要领域 1.）用于存储仿真数据的紧凑、几何无关的表示 2.）的情况。使用存储的数据进行快速的运行时数值粗化 3.）第三章用于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.）的情况。新的算法求解耦合系统的线性和非线性方程，利用上述两个。 实现这四个目标将推动我们进入由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了计算机视觉等领域一样，我设想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。

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.