Big Data for Fast and Accurate Numerical Simulation of Mechanical Structures

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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.