CAREER: Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering Design

基于物理的计算机动画和交互工程设计的多分辨率基础PI：Eitan Grinspun，哥伦比亚大学物理模拟使科学家和工程师能够研究复杂的系统，直接控制实验是昂贵的，危险的，或棘手的。探索性研究使工程师能够收集定性的直觉，或对主题系统的感觉，这反过来又会导致提出新的假设和实验方向。虽然探索过程本质上是互动的，但今天的计算障碍限制了对非互动模式的重要系统的探索。这项研究试图用新的方法克服这些障碍，这些方法快速但粗略地解决物理问题，跳过不相关的数据，只捕捉驱动设计决策的粗略变量。研究人员开发模拟技术，解决快速，交互式设计周期的愿景，特别关注薄壳柔性表面的物理模拟，如气囊，生物膜和纺织品，在汽车设计，生物医学设备优化和电影制作中的广泛应用。在协同教学的推动下，该项目培养年轻科学家对计算，数学和应用领域领域有深刻的理解，尽管需求很高，但这种技能的组合仍然很罕见。研究人员正在开发一种原则性，有条不紊的方法来粗化现有的机械系统离散几何模型，使用自适应，多分辨率分解。虽然自适应性通常是在网格细化的误差估计器的背景下研究的，但交互性表明重点关注如何最好地放弃模拟中的精度。因此，本研究（i）建立在离散微分几何领域的早期工作基础上，以制定保留关键几何和物理不变量的物理系统的粗略几何表示，（ii）研究离散微分算子的收敛性，分辨率和网格依赖性，以及（iii）有助于建立一个软件平台，用于交互式设计空间探索，并在汽车，生物医学，和电影工程

Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering DesignPI: Eitan Grinspun, Columbia UniversityPhysical simulations enable scientists and engineers to study complex systems for which direct, controlled experimentation is costly, dangerous, or intractable. Exploratory studies enable engineers to gather qualitative intuition, or feel for the subject system, which in turn leads to the posing of new hypotheses and directions for experimentation. While exploratory processes are inherently interactive, today's computational barriers limit the exploration of important systems to non-interactive modalities. This research seeks to overcome these obstacles with novel methods that quickly but coarsely resolve the physics, skipping over irrelevant data to capture only the coarse variables that drive design decisions. The investigators develop simulation techniques that address the vision of a rapid, interactive design cycle, with a specific focus on the physical simulation of thin shells flexible surfaces such as air bags, biological membranes, and textiles, with pervasive applications in automotive design, biomedical device optimization, and feature film production. In a synergistic pedagogical thrust, this project trains young scientists with a deep understanding of computation, mathematics, and application domain areas despite being in high demand, this combination of skills remains rare.The investigators are developing a principled, methodical approach to coarsening an existing discrete geometric model of a mechanical system, using adaptive, multi-resolution decompositions. Whereas adaptivity is commonly studied in the context of error estimators for mesh refinement, interactivity suggests a focus on how best to give up precision in a simulation. Therefore, this research (i) builds on early work in the field of discrete differential geometry to formulate coarse geometric representations of physical systems that preserve key geometric and physical invariants, (ii) investigates the convergence, resolution- and meshing-dependence of discrete differential operators, and (iii) contributes toward a software platform for interactive design space exploration with concrete applications in automotive, biomedical, and feature-film engineering.