aiqbench analysis
This research advances data-driven computational mechanics by integrating differentiable finite elements with structure-preserving neural networks to discover hyperelastic material laws from limited boundary observations. By embedding physical constraints like equilibrium and symmetry directly into the learning loop, the method overcomes common challenges in obtaining full-field displacement data for realistic 3D settings. The approach demonstrates robust recovery of constitutive responses across various geometries and loading conditions, marking a significant step toward physically admissible AI models in engineering science.
Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks
arXiv:2603.26517v2 Announce Type: replace-cross Abstract: The discovery of constitutive laws from experimentally accessible measurements is a central problem in nonlinear computational mechanics. Many data-driven constitutive identification approaches rely either on paired strain-stress data or on full-field displacement measurements, both of which are difficult to obtain in realistic three-dimensional settings. We present a differentiable finite element framework for the discovery of hyperelastic material laws from partial observations, including boundary-only displacement measurements and global reaction forces. The method embeds the nonlinear finite element equilibrium problem directly into the learning loop, so that candidate strain-energy densities are assessed through the deformation fields and reactions they induce. This formulation enforces mechanical equilibrium as a constraint and allows the loss function to be evaluated only at observed locations. To ensure physical admissibility and promote numerical solvability throughout training, the constitutive response is represented by Hyperelastic Neural Networks, a structure-preserving neural class that enforces residual energy and stress-free conditions, frame indifference, isotropic material symmetry, polyconvexity, coercivity, and controlled volumetric growth by construction. The resulting PDE-constrained learning problem is solved using a quasi-Newton strategy combined with continuation and solver-aware backtracking. Numerical experiments in two- and three-dimensional finite elasticity demonstrate accurate recovery of hyperelastic isotropic responses from boundary-only data, robustness to measurement noise, and generalization across geometries, loading conditions, and boundary conditions.
Abstract:The discovery of constitutive laws from experimentally accessible measurements is a central problem in nonlinear computational mechanics. Many data-driven constitutive identification approaches rely either on paired strain-stress data or on full-field displacement measurements, both of which are difficult to obtain in realistic three-dimensional settings. We present a differentiable finite element framework for the discovery of hyperelastic material laws from partial observations, including boundary-only displacement measurements and global reaction forces. The method embeds the nonlinear finite element equilibrium problem directly into the learning loop, so that candidate strain-energy densities are assessed through the deformation fields and reactions they induce. This formulation enforces mechanical equilibrium as a constraint and allows the loss function to be evaluated only at observed locations. To ensure physical admissibility and promote numerical solvability throughout training, the constitutive response is represented by Hyperelastic Neural Networks, a structure-preserving neural class that enforces residual energy and stress-free conditions, frame indifference, isotropic material symmetry, polyconvexity, coercivity, and controlled volumetric growth by construction. The resulting PDE-constrained learning problem is solved using a quasi-Newton strategy combined with continuation and solver-aware backtracking. Numerical experiments in two- and three-dimensional finite elasticity demonstrate accurate recovery of hyperelastic isotropic responses from boundary-only data, robustness to measurement noise, and generalization across geometries, loading conditions, and boundary conditions.
Numerical Analysis (math.NA); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG)
arXiv:2603.26517 [math.NA]
(or arXiv:2603.26517v2 [math.NA] for this version)
https://doi.org/10.48550/arXiv.2603.26517 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1007/s00466-026-02850-2 Focus to learn more DOI(s) linking to related resources
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