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

本构关系是描述材料对局部刺激（如应力或温度变化）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的研究至关重要。该项目试图从实际观察中推断出本构关系，而不需要在传统的实验室实验中隔离材料，这通常是昂贵的，而且很难应用于挥发性材料，如液体泡沫或材料，如海冰，只有在大尺度上表现出均质性。研究人员及其学生将开发底层算法和本构关系推理工具包（CRIKit），这是一个新的社区软件包，旨在利用机器学习和基于物理的建模的最新进展，从嘈杂的间接观察中推断本构关系，并将结果作为可引用的研究产品传播，用于一系列开源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融合中创造新的机会并增加可访问性，研究人员将通过社区外展和教育活动来强调这一点。CRIKit软件将把并行偏微分方程（PDE）求解器（如FEniCS/dolfin-adjoint）与机器学习（ML）软件包（如TensorFlow）集成在一起，从材料响应的噪声间接或原位观察中推断本构关系。前向模拟被后处理以创建合成观测值，通过损失函数与真实观测值进行比较，损失函数的范围可以从简单的最小二乘法到先进的技术，如基于ml的图像分析。这种方法导致了本构关系的非线性回归问题（表述为满足不变量和自由能兼容性要求），并依赖于PDE解算器提供的性能良好且可有效计算的梯度，该解算器使用具有伴随能力的相容离散化。推理问题揭示了每个前向模型内部和不同实验实现之间的并行性，便于优化研究。该研究使本构模型能够随时更新新的实验数据以及可重复性和验证性研究。CRIKit的模型将通过提供对本构建模前沿的随时访问来提高科学家和工程师的仿真能力。该项目由计算机与信息科学与工程理事会的先进网络基础设施办公室和数学与物理科学理事会的材料研究部提供支持。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。

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.