Applying IGANets to computational Mechanics: Fast numerical Predictions over varying Geometries

  • Obermair, Günther (TU Wien)
  • Elgeti, Stefanie (TU Wien)
  • Möller, Matthias (TU Delft)

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Fast numerical predictions are a key enabler for interactive engineering design and optimization. In today’s Finite Element Method (FEM) workflows, each design change typically requires a repeated CAD-to-analysis loop - geometry preparation, meshing, boundary condition transfer, and a new solver run - making rapid iteration difficult and turning optimization into a computational bottleneck. This contribution presents the application of IGANets (Isogeometric Analysis Networks) - a spline-based, physics-informed surrogate that aims to alleviate this loop - to test cases from structural mechanics. Once trained, IGANets enables physically-consistent near real-time evaluations directly on spline geometries, preserving the CAD-compatible representation of Isogeometric Analysis (IGA) while reducing the need for repeated full-order simulations in multi-query settings. Unlike purely data-driven surrogates, IGANets is trained by minimizing residuals of the governing equations and boundary conditions, enabling generalization beyond the geometries seen during training. This makes the method particularly attractive for design workflows where geometry is modified and updated predictions are required immediately. The method builds on isogeometric collocation. The strong-form equations are enforced at Greville-type collocation points by residual minimization. The approach is demonstrated on representative two-dimensional linear and nonlinear elasticity problems and its generalization capability across geometric variations is highlighted. In addition, first results are presented on using IGANets for material optimization via spatially varying material parameters. Accuracy and training behavior are assessed against established Galerkin-IGA and collocation reference solvers. Partial supervision with reference solutions is discussed as a means to accelerate training and improve robustness. Ongoing work targets broader generalization across geometry, material, and boundary-condition variations to support real-time design exploration.