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

Technical Report · 01 December 2020

DOI:https://doi.org/10.2172/1735693· OSTI ID:1735693

You, Huaiqian ^[1]; Yu, Yue ^[1]; Silling, Stewart A. ^[2]; D'Elia, Marta ^[3]

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1. Lehigh Univ., Bethlehem, PA (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
3. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1735693
• Report Number(s): SAND--2020-13633R; 692787
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING