1302 Model Learning and Optimization for Nonlocal and Fractional Equations

  • Yue Yu, Lehigh University
  • Marta D'Elia, Sandia National Lab
  • Xingjie Li, The University of North Carolina at Charlotte

Nonlocal models such as peridynamics and fractional equations have become a powerful tool in computational mechanics since they can describe physical phenomena that classical partial differential equations fail to capture. These effects include multiscale behavior, material discontinuities such as cracks, and anomalous phenomena such as superdiffusion and subdiffusion. For this reason, nonlocal models provide an improved predictive capability for a large class of complex engineering and scientific applications.

However, nonlocal constitutive models for materials and media are often hand tuned or rely on phenomenological engineering or scientific intuition, compromising the accuracy of predictions or their efficiency. When limited data or a priori information is available, one can resort to the solution of a control or inverse problem to recover the unknown parameters and define a more accurate, data-driven, mathematical model. This minisymposium gathers experts in computational mechanics and nonlocal models with a focus on model learning via optimal control and machine learning techniques. The central goal of the minisymposium is for researchers working with different nonlocal models to exchange ideas concerning existent and new model-identification approaches and discuss future research directions.

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