Elements: Morpho-Cyberinfrastructure for scientists and engineers studying shape change

这个项目的目标是创建一个可访问的开源软件包，Morpho，能够解决各种各样的形状优化、进化和变形问题。这些发生在跨越多个涉及软物质的NSF项目的许多系统中，软物质是易变形材料的总称，包括软机器人、塑料、复杂流体、纺织品、颗粒介质、玻璃和生物材料，以及涉及计算几何的数学和计算机科学中的其他应用。形状变化是这些系统的一个重要特征，或者是预期应用程序的一个目标，但是预测它们的行为是非常具有挑战性的。目前，在这些领域工作的从业者缺乏适当的模拟工具，这抑制了对其行为和应用程序优化的定量、机制理解。有了Morpho，领域科学家获得了一个强大的新模拟工具，使他们能够解决比目前可能的更大、更复杂的形状进化问题。该项目还通过提供广泛的培训机会，包括沉浸式年度研讨会、高质量文档和虚拟社区，创建了一个用户社区。形状优化和演化问题在数值上极具挑战性，因为最终形状事先是未知的：必须持续监控数字表示，以确保获得的解是正确的和高质量的。Morpho的核心创新是通过引入捕获网格质量概念的辅助泛函来正则化病态形状问题。这项工作的目的是扩展Morpho可以通过两种方式解决的问题的范围和复杂性。首先是允许用户合并任意类型的流形、流形上定义的场量、离散化、函数和与问题相关的约束。二是利用多层算法和GPU计算来加速模拟，并使软件能够预测给定初始配置的系统的动态响应。该项目还通过以用户为中心的开发过程和社区驱动的科学和教育计划，包括文档、示例代码和教程库、虚拟社区和年度培训研讨会，让领域科学家参与创建和使用Morpho。由此产生的软件和教育材料使其他研究人员能够模拟几个新兴领域的形状演变，这些领域涉及软物质和其他领域，包括活性材料、软机器人、可编程材料和极端力学。该奖项由NSF高级网络基础设施办公室颁发，并得到NSF数学和物理科学理事会材料研究部的联合支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The goal of this project is to create an accessible open-source software package, Morpho, able to solve a wide variety of shape optimization, evolution and shapeshifting problems. These occur in numerous systems that cut across multiple NSF programs involving soft matter, an umbrella term for readily deformable materials, and includes soft robots, plastics, complex fluids, textiles, particulate media, glasses and biological materials as well as other applications in mathematics and computer science involving computational geometry. Shape change is an important feature of these systems, or a goal of the envisioned applications, but predicting their behavior is very challenging. There is presently a lack of appropriate simulation tools readily available to practitioners working in these domains inhibiting quantitative, mechanistic understanding of their behavior and optimization for applications. With Morpho, domain scientists gain a powerful new simulation tool that enables them to tackle larger and more complex shape evolution problems than presently possible. The project also creates a user community by providing extensive training opportunities including an immersive annual workshop, high quality documentation and a virtual community.Shape optimization and evolution problems are numerically extremely challenging because the final shape is not known ahead of time: The numerical representation must be continuously monitored to ensure the solution obtained is correct and of high quality. The central innovation of Morpho is to regularize ill-posed shape problems by introducing auxiliary functionals that capture some notion of mesh quality. The aim of this work is to extend the range and complexity of problems Morpho can solve in two ways. The first is to allow the user to incorporate arbitrary types of manifolds, field quantities defined on the manifolds, discretizations, functionals and constraints pertinent to their problem. The second is to leverage multilevel algorithms and GPU computing to accelerate the simulations and enable the software to predict the dynamical response of the system given an initial configuration. The project also engages domain scientists in creating and using Morpho through a user-centered development process and a community driven science and education program, incorporating documentation, a repository of example code and tutorials, a virtual community and an annual training workshop. The resulting software and educational materials enable other researchers to simulate shape evolution in several emerging fields involving soft matter and other areas including active materials, soft robots, programmable materials and extreme mechanics. This award by the NSF Office of Advanced Cyberinfrastructure is jointly supported by the Division of Materials Research within the NSF Directorate of Mathematical and Physical Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.