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

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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.