CAREER: Next-generation Interactive Simulation

数据驱动的模型简化使物理模拟的速度有了惊人的提高。我们现在可以体验三维流体和其他复杂现象的交互模拟，这是传统技术无法实现的。然而，这种方法的主要限制是缺乏灵活性。即使对模拟域进行很小的更改，也需要完全重新计算模型。此外，该方法仅限于一小类动力系统。在这个项目中，PI寻求从根本上概括模型简化，以便它可以在运行时重新配置，处理更大范围的现象，并支持简化系统之间的异类耦合。本研究的核心目标是使交互式仿真能够以模型简化的速度进行，但又不会缺乏灵活性。这些目标之间的紧张关系揭示了根本问题。什么样的灵活性和运行时可重构性是可能的？哪些类型的简化模型最大限度地提高了运行时灵活性？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一类现象是什么？我们如何才能将跨不同系统的模型简化动态耦合在一起？对这些问题的回答将使我们更深入地理解低维表示法在什么条件下能够成功地表示复杂的动力系统。PI的方法将把他的研究目标细分为三个挑战领域：模块化和可变形基；粒子系统和非多项式动力学；以及模型耦合。在这些领域的成功将极大地提高模型简化技术的灵活性和可扩展性，使我们更接近丰富、异质的虚拟环境的交互模拟。PI还将探索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项变革性的发展，直接适用于包括医学研究、工程、工业设计、建筑、培训和教育在内的广泛具有挑战性的领域。复杂动力学的交互仿真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，为灾害情景提供时间要求严格的仿真，将是一种宝贵的教育工具。交互模拟还将允许学生玩弄遥远的现象，从摆动的蛋白质到卷曲的烟雾；交互操作这些结构将揭示为什么蛋白质的螺旋比其环更坚硬的概念。学生们甚至可以修改物理定律；将著名的力等于质量乘以加速度替换为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世界，在这个世界里，滚动的球一旦不再被推动，就会停下来。在如此不可能的世界里，抽象的方程式突然与真理产生了共鸣。

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.