aiqbench analysis
This research introduces a physics-augmented neural network architecture that enforces mechanical consistency constraints, such as polyconvexity and objectivity, directly into the training of models for anisotropic hyperelastic materials. By adapting directional features within input-convex networks, the method achieves superior extrapolation capabilities beyond the training data compared to unconstrained baselines, though with a slight trade-off in accuracy within the data range. The work advances the intersection of machine learning and computational mechanics by providing mathematically rigorous guarantees for material response predictions.
Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization
arXiv:2610.12801v1 Announce Type: cross Abstract: 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. 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). The complete energies satisfy objectivity, an exactly stress-free reference, two-dimensional polyconvexity, and prescribed growth conditions by construction, and nonnegative energy is certified separately for the selected models. 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. On the first cell, learning the features lowers the stress error sevenfold, and six features suffice on both. 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. Beyond the data, however, the Unconstrained energy loses rank-one convexity, and under confined compression it stops below half of the 500 MPa that the constrained energies reach. These results quantify what the guarantees cost in accuracy and what they secure beyond the data.
Abstract: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. 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). The complete energies satisfy objectivity, an exactly stress-free reference, two-dimensional polyconvexity, and prescribed growth conditions by construction, and nonnegative energy is certified separately for the selected models. 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. On the first cell, learning the features lowers the stress error sevenfold, and six features suffice on both. 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. Beyond the data, however, the Unconstrained energy loses rank-one convexity, and under confined compression it stops below half of the 500 MPa that the constrained energies reach. These results quantify what the guarantees cost in accuracy and what they secure beyond the data.
Computational Physics (physics.comp-ph); Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2610.12801 [physics.comp-ph]
(or arXiv:2610.12801v1 [physics.comp-ph] for this version)
https://doi.org/10.48550/arXiv.2610.12801 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 331 words
Related coverage
Amortized Neural Optimization for Pre-Layout Signal Integrity Design Space Exploration using Differentiable Surrogates
arXiv · Jun 8, 2026
Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks
arXiv · Sep 9, 2026
Validation-Gated Multi-Agent Governance for Online Adaptation of Thermal-Hydraulic Surrogate Models under Operating-Regime Shift
arXiv · Jun 3, 2026
Mind the Gap: Structure-Aware Consistency in Preference Learning
arXiv · Oct 16, 2026