IGANets: Isogeometric analysis networks and their applications to linear structural analysis problems.

Fast numerical predictions have become an indispensable component of modern engineering design workflows, whether in interactive design within computer-aided design (CAD) environments or in multi-query numerical tasks such as design optimization and uncertainty quantification. Depending on the context, "fast" may refer to near real-time predictions within a few seconds, or simply to methods that are significantly faster than high-fidelity simulations, for example those based on the finite element method (FEM). With the aim of providing a tool that not only enables such accelerated predictions but also integrates seamlessly into established workflows, we introduce the concept of IGANets. IGANets are spline-based, physics-informed machine learning models that can be integrated naturally between CAD representations and numerical analysis tools, particularly those based on isogeometric analysis (IGA). Unlike purely data-driven approaches, IGANets do not inherently rely on precomputed training data; instead, they are formulated in a collocation setting directly from physical models. In this paper, we present the IGANets concept and demonstrate its feasibility through numerical experiments for the Poisson equation and linear elasticity. In addition, we investigate a multi-instance linear-elasticity setting with varying I-beam-like geometries and boundary conditions in order to assess the generalization capability of the framework. The results show that IGANets can predict solutions for previously unseen problem instances within the training range with improved accuracy as the number of training samples increases.