CAREER: Next-generation Interactive Simulation

数据驱动的模型简化使物理模拟的速度惊人。我们现在可以体验三维流体和其他传统技术无法实现的复杂现象的交互式模拟。然而，这种方法的主要限制是缺乏灵活性。即使对仿真域进行很小的更改也需要对模型进行完全的重新计算。此外，该方法仅限于一小类动力系统。在这个项目中，PI试图从根本上推广模型简化，以便在运行时可重新配置，处理更大范围的现象，并支持简化系统之间的异构耦合。本研究的核心目标是使交互式仿真具有模型简化的速度，但没有其缺乏灵活性。这些目标之间的紧张关系揭示了一些基本问题。什么样的灵活性和运行时可重构性是可能的？哪种简化模型能最大限度地提高运行时灵活性？如何将动力系统投射到这些模型上？我们可以应用模型简化的最广泛的现象类别是什么？我们如何跨异构系统耦合模型简化动力学？诸如此类问题的答案将提供对低维表示能够成功表示复杂动力系统的条件的更深入理解。PI的方法是将他的研究目标细分为三个挑战领域：模块化和可变形的基础；粒子系统与非多项式动力学；还有模型耦合。在这些领域的成功将大大增加模型简化技术的灵活性和可扩展性，使我们更接近丰富的、异构的虚拟环境的交互式仿真。PI还将探索由这些理论进步带来的几项先进技术。更广泛的影响：解决这些挑战将是一个变革性的发展，直接适用于广泛的具有挑战性的领域，包括医学研究、工程、工业设计、建筑、培训和教育。复杂动力学的交互式模拟将使人们能够快速探索物理设计空间，改进飞机和其他非线性系统的控制器，为危险或远程环境提供培训，为灾难场景提供时间关键模拟，并将成为一种有价值的教育工具。交互式模拟还将允许学生玩远程现象，从摆动的蛋白质到卷曲的烟雾；交互操作这些结构将揭示一些概念，比如为什么蛋白质的螺旋比它的环更坚硬。学生甚至可以修改物理定律；把著名的力等于质量乘以加速度替换成力等于质量乘以速度，你会发现自己置身于一个奇怪的糖蜜般的世界，一个滚动的球一旦不再被推动就会静止。在这样一个不可能的世界里，抽象的方程式突然与真理产生共鸣。

Data-driven model reduction has enabled astonishing speedups in physical simulation. We can now experience interactive simulations of three-dimensional fluids and other complex phenomena that were impossible with traditional techniques. However, this approach's central limitation is inflexibility. Even small changes to the simulation domain require complete recomputation of the model. Moreover, the approach has been limited to a small class of dynamical systems. In this project, the PI seeks to radically generalize model reduction so that it is reconfigurable at runtime, handles a far greater range of phenomena, and supports heterogeneous coupling between reduced systems. The core goal of this research is to enable interactive simulations with the speed of model reduction, but without its inflexibility. The tension between these goals brings to light fundamental questions. What kinds of flexibility and runtime reconfigurability are possible? What kinds of reduced models maximize runtime flexibility? How can dynamical systems be projected onto these models? What is the broadest possible class of phenomena to which we can apply model reduction? How can we couple the model reduced dynamics across heterogeneous systems? The answers to questions such as these will provide a deeper understand of the conditions under which low-dimensional representations can successfully represent complex dynamical systems. The PI's approach will be to subdivide his research goals into three challenge areas: modular and deformable bases; particle systems and non-polynomial dynamics; and model coupling. Success within these areas will greatly increase the flexibility and extensibility of model reduction techniques, bringing us closer to interactive simulation of rich, heterogeneous virtual environments. The PI will also explore several advanced technologies enabled by these theoretical advances.Broader Impacts: Solving these challenges will be a transformative development directly applicable to a wide range of challenging fields including medical research, engineering, industrial design, architecture, training, and education. The interactive simulation of complex dynamics will allow people to rapidly explore physical design spaces, improve controllers for airplanes and other nonlinear systems, provide training for dangerous or remote environments, provide time-critical simulation for disaster scenarios, and will be a valuable tool for education. Interactive simulation will also allow students to play with remote phenomena, from wiggling proteins to curling smoke; interactively manipulating these structures will reveal concepts such as why a protein's helices are more rigid than its loops. Students could even modify the laws of physics; replace the famous force equals mass times acceleration with force equals mass times velocity and you find yourself in a strange molasses-like world where a rolling ball comes to rest as soon as it's no longer being pushed. In such impossible worlds, abstract equations suddenly resonate with truth.