Collaborative Research: Elements: Software: NSCI: Constitutive Relation Inference Toolkit (CRIKit)

协作研究：要素：软件：NSCI：本构关系推理工具包 (CRIKit)

• 批准号: 1835792
• 负责人: Tobin Isaac
• 金额: $ 29.91万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1835792&HistoricalAwards=false
• 关键词: Collaborative; Research; Elements; Software; NSCI

Constitutive relations are mathematical models that describe the way materials respond to local stimuli such as stress or temperature change, and are essential to the study of biological tissues in biomechanics, ice and rock in geosciences, plasmas in high-energy physics and many other science and engineering applications. This project seeks to infer constitutive relations from practical observations without requiring isolation of the material in conventional laboratory experiments, which are often expensive and difficult to apply to volatile materials such as liquid foams or materials such as sea ice that exhibit homogenized behavior only at large scales. The investigators and their students will develop underlying algorithms and the Constitutive Relation Inference Toolkit (CRIKit), a new community software package to leverage recent progress in machine learning and physically-based modeling to infer constitutive relations from noisy, indirect observations, and disseminate the results as citable research products for use in a range of open source and extensible commercial simulation environments. This development will create new opportunities and increase accessibility at the confluence of data science and high-fidelity physical modeling, which the investigators will highlight through community outreach and educational activities.The CRIKit software will integrate parallel partial differential equation (PDE) solvers like FEniCS/dolfin-adjoint with machine learning (ML) packages like TensorFlow to infer constitutive relations from noisy indirect or in-situ observations of material responses. The forward simulation is post-processed to create synthetic observations which are compared to real observations by way of a loss function, which may range from simple least squares to advanced techniques such as ML-based image analysis. This approach results in a nonlinear regression problem for the constitutive relation (formulated to satisfy invariants and free energy compatibility requirements) and relies on well-behaved and efficiently computable gradients provided by PDE solvers using compatible discretizations with adjoint capability. The inference problem exposes parallelism within each forward model and across different experimental realizations and facilitates research in optimization. The research enables constitutive models to be readily updated with new experimental data as well as reproducibility and validation studies. CRIKit's models will improve simulation capability for scientists and engineers by providing ready access to the cutting edge of constitutive modeling.This project is supported by the Office of Advanced Cyberinfrastructure in the Directorate for Computer & Information Science & Engineering and the Division of Materials Research in the 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.

构成关系是数学模型，描述了材料对局部刺激的反应方式，例如压力或温度变化，对于研究地球科学中生物力学，冰和岩石的生物组织，高能物理学中的等离子体以及许多其他科学和工程和工程应用至关重要。该项目试图从实际观察结果中推断出构型关系，而无需在常规实验室实验中隔离材料，这些实验实验通常很昂贵且难以应用于挥发性材料，例如液体泡沫或诸如海冰等材料，这些材料仅在大尺度上表现出同质性行为。调查人员及其学生将开发潜在的算法和构成关系推理工具包（CRIKIT），这是一种新的社区软件包，以利用机器学习和基于物理的建模的最新进展，从噪音，间接观察结果中推断构型关系，并将结果作为可疑的研究产品传播为开源商业模拟环境的范围，以将结果传播为Citable研究产品。这一发展将创造新的机会，并在数据科学和高保真物理建模的汇合处增加可访问性，研究人员将通过社区外展和教育活动来强调，Crikit软件将平行的部分微分方程（PDE）溶解器（PDE）溶解器（PDE）将Fenics/dolfin-Adoctions（如机器学习（ML）与Superiation copteration（ML）相关的材料相关性，从而将其整合到诸如selliserflow之类的材料中，以此为目的。回答。进行后期处理以创建合成观测值，这些观测值与损失函数的真实观测值进行了比较，损耗函数可能范围从简单的最小二乘正方形到高级技术，例如基于ML的图像分析。这种方法导致本构之间关系的非线性回归问题（为满足不变性和自由能兼容性要求而制定），并依赖于PDE求解器使用具有兼容的离散化的邻接能力的PDE求解器提供的良好行为且有效地计算的梯度。推论问题在每个远期模型和不同的实验实现中暴露了并行性，并促进了优化研究。该研究使本构模型可以通过新的实验数据以及可重复性和验证研究轻松更新。克里克特（Crikit）的模型将通过准备好访问本构建模型的前沿来提高科学家和工程师的模拟能力。该项目得到了计算机与信息科学与工程局高级网络基础设施办公室的支持，以及通过数学奖的构建机构的构建机构的构建委员会的支持，并在计算机上的材料研究部提供了材料研究。更广泛的影响审查标准。