CHS: Small: Real-Time Simulation of Elastic Solids

现代电影中的视觉效果表明，基于离线物理的模拟达到的质量通常无法与真实视频片段区分开来。然而，在手术模拟器等实时应用中，情况正好相反，即使是非专家用户也可以很快发现与参考视频记录相比，模拟中的不足之处。PI在这个项目中的目标是为下一代手术模拟器奠定算法基础，这将减少外科医生在真实病人或动物身上练习的需要。在生物力学应用中，有限元软件包经常因运行时间过慢而受到批评。PI的新数值方法将导致更快速的迭代，使生物力学研究人员能够在更短的时间内测试更多的假设。快速物理在电脑动画产业中也会受到高度赞赏，因为目前的方法对于具有精确皮肤和肉体弹性的互动角色摆姿势来说太慢了。虚拟现实是一个新兴而又日益重要的应用领域。实时物理对于从训练模拟器到创造性应用（如服装设计）和游戏等虚拟现实应用的推动是必要的，后者对于普及数学、物理和计算机科学特别有用，从而为教育和推广开辟了新的机会。运动方程的数值时间积分的现代通用方法，通常用于离线仿真，具有先进的误差控制机制，同时努力最大化计算效率。然而，基于实时物理的仿真技术必须符合一组不同的需求。特别是，数值积分算法必须能够在只使用少量计算资源的情况下推进仿真。诸如手术模拟器之类的交互式应用程序通常需要至少每秒30帧才能产生平滑运动的幻觉。这使得实时物理计算具有挑战性，即使使用现代cpu和gpu。为了应对这一挑战，已经为娱乐应用程序（游戏）开发了专门的算法，其中准确性不太重要。在这项研究中，PI将研究新的数值时间积分算法，这些算法满足实时物理的困难计算约束，但最大限度地提高精度，特别关注弹性固体（如生物软组织）的模拟。尽管它们具有复杂的非线性材料特性，但PI最近的工作表明，对详细模型的精确实时模拟是可以实现的。特别是，虽然使用牛顿方法进行数值求解的隐式积分方案是基于物理模拟的传统计算工具，但PI的结果表明，牛顿方法并不总是最有效的方法，特别是在实时设置中。隐式时间步进可以表述为一个优化问题，它将基于物理的仿真与数学优化联系起来，开辟了许多有趣的研究机会。即使是简单的机械系统也需要非凸目标函数，这一事实使情况变得复杂。实时应用程序不提供第二次修正错误结果的机会，因此，必须在不增加计算复杂性的情况下避免模拟不稳定。所有的数值积分方案都不可避免地会由于时间离散而产生误差，而在困难的情况下，由于实时计算的限制，这种误差可能会进一步加剧。该项目将寻求发现新的数值方法，同时满足1)实时计算，2)稳定性和3)精度的要求，同时支持真实的材料模型。

Visual effects in modern films demonstrate that offline physics-based simulations achieve quality which often cannot be distinguished from real video footage. However, the opposite is true in real-time applications such as surgery simulators, where even non-expert users can quickly notice deficiencies in the simulation when compared to reference video recordings. The PI's goal in this project is to lay the algorithmic foundations for the next generation of surgery simulators, which would reduce the need for surgeons to practice on real patients or animals. In biomechanics applications, finite element software packages are often criticized for slow running times. The PI's new numerical methods will lead to more rapid iterations, allowing biomechanics researchers to test more hypotheses in less time. Fast physics would also be highly appreciated in the computer animation industry, because current methods are too slow for interactive character posing with physically accurate elasticity of skin and flesh. Virtual reality is a new but increasingly important application area. Real-time physics will be necessary to power virtual reality applications ranging from training simulators to creative applications (e.g., clothing design) and games, the latter being particularly useful for popularizing mathematics, physics, and computer science, thereby opening up new opportunities for education and outreach.Modern general-purpose methods for the numerical time integration of the equations of motion, typically used for offline simulation, feature advanced mechanisms for error control while striving to maximize computational efficiency. However, real-time physics-based simulation techniques must conform to a different set of requirements. In particular, the numerical integration algorithm must be able to advance the simulation while using only a small amount of computing resources. Interactive applications such as surgery simulators typically require at least 30 frames per second to create the illusion of smooth motion. This makes real-time physics computationally challenging, even with modern CPUs and GPUs. To cope with this challenge, specialized algorithms have been developed for entertainment applications (games), where accuracy is less critical. In this research the PI will study new numerical time integration algorithms which meet the difficult computational constraints of real-time physics but maximize accuracy, with a specific focus on the simulation of elastic solids such as biological soft tissues. Despite their complex nonlinear material properties, the PI's recent work suggests that accurate real-time simulations of detailed models are within reach. In particular, whereas implicit integration schemes, numerically solved using Newton's method, are the traditional computational workhorses of physics-based simulations, the PI's results demonstrate that Newton's method is not always the most effective approach, especially in the real-time setting. Implicit time stepping can be formulated as an optimization problem, which connects physics-based simulation with mathematical optimization, opening up many interesting research opportunities. The situation is complicated by the fact that even simple mechanical systems require non-convex objective functions. Real-time applications do not offer a second chance to fix incorrect results and, therefore, it is imperative to avoid simulation instability - without increasing computational complexity. All numerical integration schemes inevitably incur error due to time discretization and in difficult scenarios such error may be further exacerbated due to the real-time computing constraints. This project will seek to discover new numerical methods which simultaneously satisfy requirements of 1) real-time computing, 2) stability, and 3) accuracy, while supporting realistic material models.