CHS: Small: Real-Time Simulation of Elastic Solids

现代电影中的视觉效果表明，离线基于物理的模拟达到的质量往往无法与真实的视频片段区分开来。 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在与参考视频记录相比时迅速注意到模拟中的缺陷。 PI在该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的患者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慢而受到批评。 PI的新数值方法将导致更快的迭代，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。 快速物理学在计算机动画行业也会受到高度赞赏，因为目前的方法对于具有皮肤和肉体的物理精确弹性的交互式角色姿势来说太慢了。 虚拟现实是一个新的但越来越重要的应用领域。 实时物理将是必要的，以推动虚拟现实应用程序，从培训模拟器到创造性的应用程序（例如，服装设计）和游戏，后者对普及数学、物理学和计算机科学特别有用，从而为教育和推广提供了新的机会。运动方程的数值时间积分的现代通用方法通常用于离线模拟，其特点是先进的误差控制机制，同时努力最大化计算效率。 然而，基于物理的实时仿真技术必须符合不同的要求。 特别是，数值积分算法必须能够在仅使用少量计算资源的情况下推进模拟。 交互式应用程序，如手术模拟器，通常需要至少每秒30帧，以创建平滑运动的错觉。 这使得实时物理计算具有挑战性，即使使用现代CPU和GPU也是如此。 为了科普这一挑战，已经为娱乐应用（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，满足实时物理学的困难计算约束，但最大限度地提高精度，特别侧重于模拟弹性固体，如生物软组织。 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，而隐式积分计划，数值求解使用牛顿的方法，是传统的计算基于物理的模拟的主力，PI的结果表明，牛顿的方法并不总是最有效的方法，特别是在实时设置。 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相结合，开辟了许多有趣的研究机会。 由于即使是简单的机械系统也需要非凸的目标函数，因此情况变得复杂。 实时应用程序不会提供第二次修复错误结果的机会，因此，必须避免模拟不稳定-而不会增加计算复杂性。 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，并且在困难的情况下，由于实时计算的约束，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）准确性的要求，同时支持现实的材料模型。

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.