CAREER: Interactive Physically Based Animation and Optimal Control Using Model Reduction

职业：基于交互物理的动画和基于模型简化的最优控制jernej Barbic，南加州大学计算机科学系【摘要】自然界中的许多动力系统在其基础方程方面是相当容易理解的，但是用详细的模型进行模拟是非常缓慢的。例如，有限单元法（FEM）已被广泛用于模拟人体组织、汽车和飞机的机械部件、建筑结构或电脑游戏中的角色。然而，现实世界的系统非常复杂，通常需要大型计算机处理能力来进行模拟、控制和优化。本研究探讨了用简单的数学原理模型来近似复杂物理的系统方法。由此产生的快速仿真和控制可以使医疗培训更具沉浸感，计算机游戏更具娱乐性，CAD/CAM更快更可靠。更一般地说，这项工作适用于任何由微分方程控制的系统，在机器人、航空和国防系统中有更广泛的应用。除了开发新的公开可用的课程材料外，教育活动还包括在开源许可下向世界发布大型c++计算机图形/动画代码库，并访问洛杉矶欠发达地区的高中，让学生接触到科学和工程职业的好处。研究人员使用模型简化来解决材料和几何复杂性，这种方法通过对适当选择的低维空间的投影来近似完整的运动方程。虽然非线性系统的模型约简以前已经应用于计算机图形学和其他学科，但现有的算法往往缺乏灵活性，不能在空间或时间上自适应，并且只能提供平滑的低维输出，即使已知未约简的输出是复杂的。研究人员利用拉格朗日力学、多分辨率分析和非线性优化等技术来研究如何克服这些限制。最终目标是加速物理，使物理和设计的融合成为可能，用于大型，复杂的计算机图形和工程实践系统。

CAREER: Interactive Physically Based Animation and Optimal Control Using Model ReductionJernej Barbic, Computer Science Department, University of Southern CaliforniaAbstractMany dynamical systems in nature are reasonably well-understood in terms of their underlying equations, but are very slow to simulate with detailed models. For example, the Finite Element Method (FEM) has been used extensively to simulate human tissue, automobile and airplane mechanical components, architectural structures, or characters in a computer game. Real-world systems are, however, very complex, which normally requires large computer processing power for their simulation, control and optimization. This research investigates systematic approaches to approximate complex physics with simple, yet mathematically principled models. The resulting fast simulation and control can make medical training more immersive, computer games more entertaining, and CAD/CAM faster and more reliable. More generally, this work applies to any system governed by differential equations, with broader applications in robotics, aeronautics, and defense systems. In addition to developing new publicly available coursework material, educational activities include releasing a large C++ computer graphics/animation codebase to the world under an open source license, and visits to high schools in under-deserved areas of Los Angeles where students are exposed to the benefits of careers in science and engineering.The investigators tackle material and geometric complexity using model reduction, an approach where full equations of motion are approximated by a projection to a properly selected low-dimensional space. While model reduction of nonlinear systems has been previously employed in computer graphics and other disciplines, the existing algorithms often lack flexibility, are not adaptive in space or time, and can only provide smooth, low-dimensional output, even if the unreduced output is known to be complex. The investigators study how to overcome these limitations, using techniques from Lagrange mechanics, multi-resolution analysis and nonlinear optimization. The ultimate goal is to accelerate physics to the point where fusion of physics and design becomes possible for large, complex systems of computer graphics and engineering practice.