Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
This work provides an incremental improvement in the accuracy of stress wave simulations for engineers and researchers working with composite materials.
This paper addresses the challenge of accurately simulating stress waves in one-dimensional composite materials by learning nonlocal constitutive laws. The authors developed an optimization-based technique using Bernstein polynomials to approximate the nonlocal kernel function, resulting in a homogenized nonlocal continuum model that accurately reproduces wave motion from high-fidelity data.
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.