New paper is available online now

The article 'Geometrically-informed generative adversarial networks as Newton–Raphson initializers for closest point projection in point-to-surface contact', written by Ankit, Deep Haloi, Saurav Sukla Baidya, Roger Andrew Sauer, Sachin Singh Gautam, has been published in Elsevier's 'Computer Methods in Applied Mechanics and Engineering'.

Abstract:
The local closest-point projection (CPP) step in quadrature point-to-surface and node-to-surface contact formulations requires nested Newton–Raphson (NR) iterations to determine the parametric coordinates of a slave point on the master surface, and constitutes a recurring computational cost in large-scale contact simulations. This work investigates the use of conditional Generative Adversarial Networks (GANs) to accelerate CPP computation on quadrilateral master surface patches, both as direct surrogates and as geometry-informed initializers within a GAN-NR hybrid strategy. Three conditional GAN variants are developed and compared: a conditional GAN (cGAN), a conditional Wasserstein GAN with gradient penalty (cWGAN-GP), and a novel Geometrically Informed GAN (GI-GAN), which embeds isoparametric surface-consistency and tangential orthogonality constraints directly into the generator objective. Trained on a modest dataset of high-fidelity NR-computed CPP solutions on bilinear quadrilateral (Q4) patches, the models are evaluated through aggregate relative error, kernel density estimation, SHAP-based interpretability analysis, regime-wise boundary sensitivity, and computational efficiency metrics.

GI-GAN consistently achieves the lowest aggregate relative error (E_rel≈0.123–0.149), the closest distributional agreement with the NR reference, and the most faithful preservation of geometric feature influence as confirmed by SHAP attribution. In direct CPP mode, cWGAN-GP and GI-GAN yield one to two orders of magnitude acceleration over the conventional NR solver, with GI-GAN attaining a peak speed-up of 57.766 times. In the GAN-NR hybrid strategy, the GAN prediction serves exclusively as an improved initial guess, and the hybrid solution is identical in accuracy to the conventional NR procedure. GI-GAN achieves a consistent 19%–21% reduction in total wall-clock time and approximately 37%–38% reduction in NR iterations across all tested sample sizes, at no additional approximation cost. Robustness of the hybrid strategy is further validated on a range of benchmarks. These include controlled edge-to-edge and corner-to-corner benchmarks with varying fractions of boundary-dominated CPP cases, and a connected piecewise bilinear multi-element surface. Curved-surface benchmarks using serendipity quadrilateral (Q8) elements are also considered, covering a half-cylinder, a sinusoidally modulated tubular surface, and a self-contact-inspired wavy tubular shell. All benchmarks yield strictly positive computational gains. Notably, the Q4-trained GI-GAN transfers directly to Q8 curved geometries without retraining, demonstrating robustness beyond its training domain.

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https://authors.elsevier.com/c/1nurAAQEJCnYD