Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

• URL: http://arxiv.org/abs/2012.04157v1
• Date: Tue, 8 Dec 2020 01:46:26 GMT
• Title: Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
• Authors: Huaiqian You, Yue Yu, Stewart Silling, Marta D'Elia
• Abstract summary: We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal laws for stress wave propagation models.
• Score: 3.1196544696082613
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

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