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

本构关系是描述材料对应力或温度变化等局部刺激的响应方式的数学模型，对于生物力学中的生物组织、地球科学中的冰和岩石、高能物理中的等离子体以及许多其他科学和工程应用是必不可少的。该项目寻求从实际观察中推断本构关系，而不需要在常规实验室实验中隔离材料，这些实验通常昂贵且难以应用于挥发性材料，如液体泡沫或仅在大范围内表现出均质行为的材料，如海冰。研究人员和他们的学生将开发基本算法和本构关系推理工具包(CRIKit)，这是一个新的社区软件包，利用机器学习和基于物理的建模的最新进展，从嘈杂的间接观测中推断本构关系，并将结果作为可引用的研究产品传播，用于一系列开放源代码和可扩展的商业模拟环境。这一发展将在数据科学和高保真物理建模的交汇处创造新的机会并增加可获得性，研究人员将通过社区推广和教育活动来强调这一点。CRIKit软件将集成像FENICS/Dolfin-Adjun这样的并行偏微分方程(PDE)求解器和像TensorFlow这样的机器学习(ML)包，以从对材料响应的嘈杂的间接或现场观察中推断本构关系。正向模拟被后处理以创建合成观测值，该合成观测值通过损失函数与真实观测值进行比较，该损失函数的范围可以从简单的最小二乘到诸如基于ML的图像分析的高级技术。这种方法导致了本构关系的非线性回归问题(公式以满足不变量和自由能相容要求)，并依赖于由PDE求解器使用具有伴随能力的相容离散提供的行为良好且可高效计算的梯度。推理问题揭示了每个正向模型内部和不同实验实现之间的并行性，并促进了优化研究。这项研究使本构模型能够很容易地用新的实验数据以及重复性和有效性研究进行更新。CRIKIT的模型将通过提供对本构模型尖端的便捷访问，提高科学家和工程师的模拟能力。该项目由计算机和信息科学与工程局的高级网络基础设施办公室和数学和物理科学局的材料研究部支持。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为是值得支持的。

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.