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USACM Nanotechnology Virtual Seminar
Wednesday, September 28, 2022, 2:00 PM - 3:00 PM CDT
Category: Events

USACM Nanotechnology Virtual Seminar

Geometric Learning for Discovering Complex Material Behaviors of Microstructures


Steve WaiChing Sun, Columbia University


Amartya Banerjee, University of California, Los Angeles



Plasticity models often include a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. However, a surface can also be represented explicitly by a manifold of which the tangential space is Euclidean. In this work, we introduce the concept of yielding manifold. This yielding manifold is reconstructed by stitching local multi-resolution patches together. This treatment enables us to construct a highly complex and precise yield envelope by breaking it down into multiple coordinate charts. The global atlas is then built to enforce the consistency of the machine learning generated yield surface. In contrast to data from smooth manifolds, data collected from sensors and numerical simulations are often discrete. As such, we propose to use graph embedding to create latent space inferred from 3D microstructural data represented via weighted graphs. Vectors of this latent space are used as both geometrical descriptors and internal variables of which a decoder can be used to convert predictions in the latent space back as a weight graph. This approach establishes a direct connection between nonlinear dimensional reduced simulations with machine learning constitutive models. Potential applications of geometric reinforcement learning for inverse problems and the design of experiments in the limited data regime will also be discussed.