arXiv：cs.LG· S. Ares de Parga, A. Cornejo, J. A. Hern\'andez, R. Rossi·· 13 小时前
基于成对方向特征的多凸物理增强神经网络：各向异性超弹性均匀化代理模型
Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization
AI 导读
研究人员提出一种基于成对方向特征的多凸物理增强神经网络（PANN），其方向、拉伸幂次与行列式指数可自适应 RVE 响应，特征与逐分量非递减凸核（ICNN 或 ICKAN）复合，构造上即满足客观性、无应力参考态、二维多凸性与指定增长条件。
正文
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.
| Comments: | 38 pages, 15 figures |
| Subjects: | Computational Physics (physics.comp-ph); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2610.12801 [physics.comp-ph] |
| (or arXiv:2610.12801v1 [physics.comp-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12801 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sebastian Ares De Parga Regalado Dr. [view email]
[v1]
Thu, 8 Oct 2026 23:15:04 UTC (3,255 KB)
来源：arXiv：cs.LG · arxiv.org