Big Data for Fast and Accurate Numerical Simulation of Mechanical Structures

对物理现象的数值模拟，如大变形和小变形，对于从建筑设计到3D打印的一切都是至关重要的工具。对某些事物在现实世界中的表现的了解对设计过程具有巨大的影响。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所需精度施加的限制和先进添加剂制造技术的高分辨率、多材料性质带来的计算挑战时。*当人们考虑到下一代建筑、飞机、汽车甚至大片中的角色的交互设计工具都渴望“在回路中”模拟时，这个问题就变得更加令人望而生畏。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关于设计更改效果的反馈；第二，超快的模拟为智能的、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后台探索，以便找到满足设计师约束的非直观设计。*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，就会被丢弃。但为什么会出现这种情况呢？我们可以用一个庞大的模拟数据数据库来做什么？我们可以使用它来加速大范围的模拟，而不需要在个案的基础上进行冗长而昂贵的预计算吗？在这个研究项目中，我将探索这个问题的含义，并开发模拟算法，使用从这样的数据库中提取的先验信息来避免传统方法的性能和保真度之间的权衡。这样的算法对使用物理模拟的任何领域都有太多的好处。*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、与几何无关的表示*2。)使用存储的数据进行快速、运行时的数值粗化*3。)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。)求解线性和非线性耦合方程组的新算法，它利用了上述两种方法。*实现这四个目标将把我们推向由大数据驱动的高性能物理模拟的新时代。就像在线数据库如何给计算机视觉等领域带来革命性的变化一样，我预计数值物理和计算机动画社区也将发生类似的变化。我认为，这项工作本质上是为模拟数据建立谷歌图像搜索，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.