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 Grspirun，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，对于这些系统，直接的受控实验是昂贵、危险或难以处理的。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，这反过来又导致提出新的假设和实验方向。虽然探索过程本质上是交互的，但今天的计算障碍将对重要系统的探索限制在非交互形态上。这项研究试图用快速但粗略地解决物理问题的新方法来克服这些障碍，跳过不相关的数据，只捕获驱动设计决策的粗略变量。研究人员开发了模拟技术，以解决快速、交互设计周期的愿景，特别关注薄壳柔性表面的物理模拟，如安全气囊、生物膜和纺织品，在汽车设计、生物医学设备优化和故事片制作中广泛应用。在协同教学的推力下，这个项目培养年轻科学家对计算、数学和应用领域有深刻的理解，尽管需求很高，但这种技能的组合仍然很少见。研究人员正在开发一种原则性的、有条不紊的方法来粗化现有的机械系统的离散几何模型，使用自适应的、多分辨率的分解。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，但交互性建议关注如何最好地在模拟中放弃精度。因此，这项研究(I)建立在离散微分几何领域的早期工作的基础上，以保持关键的几何和物理不变量的物理系统的粗略几何表示为基础，(Ii)研究离散微分算子的收敛、分辨率和网格依赖，以及(Iii)为交互式设计空间探索的软件平台做出贡献，并在汽车、生物医学和功能电影工程中进行具体应用。

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.