Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization

Key points

• This work develops a polyconvex physics-augmented neural network (PANN) construction based on paired directional features whose orientations, stretch powers, and determinant exponents adapt to the RVE response.1
• The features are composed with convex, componentwise nondecreasing cores, realized as an input-convex neural network (ICNN) or an input-convex Kolmogorov-Arnold network (ICKAN).1
• On a multicavity and a single-cavity periodic cell, these energies are compared with an Unconstrained energy, trained identically without the curvature and growth constraints, and with three hyperreduced projection-based reduced-order models (HPROMs), which serve as physics-based references.1
• The constrained energies remain below one percent in stress error and in the displacement error of a tensile-coupon FE$^2$ application with a full-order reference, whereas the Unconstrained energy and the HPROMs are more accurate inside the data.1

Sources (1)

• [1]Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 11:15 PM

  Approximating the effective anisotropic hyperelastic response of a representative volume element (RVE) requires constitutive expressiveness, mechanical consistency, and computational efficiency.

  This work develops a polyconvex physics-augmented neural network (PANN) construction based on paired directional features whose orientations, stretch powers, and determinant exponents adapt to the RVE response.

Extractive summary: sentences quoted from the sources.