Metamaterials design by ML

To this end, we introduced a novel data-driven approach based on the integration of two neural networks (now colloquially known as "tandem neural networks") for the forward- and inverse-problems that renders the inverse design challenge well-posed. This approach, in contrast to surrogate optimization methods, provides a computationally inexpensive two-way relationship between design parameters and mechanical properties.  We applied this framework to a diverse range of metamaterial classes for tunable mechanical response (anisotropic stiffness only being the tip of the iceberg) as shown below.

When the design is non-parametric or uninterpretable?

Despite the advances, ML for metamaterials design is facing some critical bottlenecks namely, what if the design parameterization and property representation are

• extremely high-dimensional,

• uninterpretable (e.g., text- or graph-based) to a numerical optimization algorithm, and/or

• discrete and discontinuous (e.g., ad-hoc truss- and plate-based lattices)?

For example, most truss lattices are based on well-known topologies such as the diamond, kagome, octahedron, or honeycomb lattices, which follow ad-hoc naming and hardly any rigorous design conventions. Specifically, each of those topologies can be described by a finite set of design parameters, which, however, do not generalize to other topologies. Consequently, most design optimization methods for truss lattices to date have focused on only a small pool of selected topologies, which leads to suboptimal solutions and fails to exploit the full range of available lattice structures. An alternative is the representation of a truss unit cell by voxels, which capture the presence (or lack) of material in a rasterized 3D space. Since the effective material properties are generally highly sensitive to the underlying structure, any such lattice parameterization based on voxelization requires high-resolution images and is hence computationally infeasible.

To address these challenges, we introduced a general ML framework for inverse design of metamaterials with high-dimensional and/or non-trivial parameterizations. The framework generally consists of two ML models – one to construct a low-dimensional, continuous latent representation unifying an enormous range of metamaterial designs; another one to map this unified latent space to properties of interest. Leveraging specially designed realizations of the general ML framework, we inverse designed metamaterials based on graph or textual representations. This is best represented by our recent work on designing graph-based truss lattices for metamaterials with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, and tailored stress-strain behaviors.

Full constitutive modeling from scarce loading data

When it comes to nonlinear mechanical behavior, one is generally interested in the effective constitutive model (i.e., stress as a function of arbitrary strain) of a metamaterial. However, all existing physics-based or data-driven models for (truss) metamaterials have been restricted to either a single type of lattice or predicting the stress-strain response along specific loading directions, e.g., uniaxial compression/tension. In pursuit of a general constitutive model, we introduced HyperCAN, a machine learning framework that utilizes hypernetworks to construct adaptable constitutive artificial neural networks for a wide range of beam-based metamaterials exhibiting diverse mechanical behavior under finite deformations. This unified framework demonstrates robust generalization in predicting the mechanical behavior of previously unseen metamaterial designs and loading scenarios well beyond the training domain. We show how HyperCAN can be integrated into multiscale simulations to accurately capture the highly nonlinear responses of large-scale truss metamaterials, closely matching fully resolved simulations while significantly reducing computational costs. This offers new efficient opportunities for the multiscale design and optimization of truss metamaterials.