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

职业：使用模型简化的交互式基于物理的动画和最优控制Jernej Barbic，计算机科学系，南加州大学摘要自然界中的许多动力系统在其基本方程方面是相当好理解的，但是用详细的模型来模拟非常慢。例如，有限元方法（FEM）已被广泛用于模拟人体组织、汽车和飞机机械部件、建筑结构或计算机游戏中的角色。然而，现实世界的系统是非常复杂的，这通常需要大量的计算机处理能力来进行仿真，控制和优化。 这项研究调查了系统的方法来近似复杂的物理与简单的，但数学原理模型。由此产生的快速模拟和控制可以使医疗培训更加身临其境，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。除了开发新的公开课程材料外，教育活动还包括在开源许可下向全世界发布大型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。一种方法，其中完整的运动方程通过投影到适当选择的低维空间来近似。虽然非线性系统的模型简化以前已经在计算机图形学和其他学科中采用，但现有的算法通常缺乏灵活性，在空间或时间上不自适应，并且只能提供平滑的低维输出，即使已知未简化的输出是复杂的。研究人员研究如何克服这些限制，使用技术从拉格朗日力学，多分辨率分析和非线性优化。最终目标是加速物理学，使物理学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.