SplineNet: An Isogeometric Deep Learning Method for Complex Shells

2026-07-07

AI Summary

This work addresses the inefficiency and geometric inaccuracy inherent in traditional CAD/CAE workflows for shell structures by proposing a novel integration of isogeometric analysis and deep learning. The method employs watertight T-splines to construct a geometrically exact neural network architecture, uniquely embedding Bézier extraction and Bernstein polynomials as activation functions within the DeepONet framework. Coupled with the Kirchhoff–Love shell formulation, this approach enables seamless unification of CAD and CAE within a single neural network. Without requiring repeated modeling or retraining, the model efficiently and accurately predicts mechanical responses across diverse complex shell geometries, substantially enhancing both computational efficiency and solution accuracy.

Abstract

We present a novel isogeometric deep learning method, termed SplineNet, for the seamless design and analysis of shell structures with complex geometries. The proposed approach is built upon watertight spline representations, e.g., analysis-suitable unstructured T-splines, and features exact geometric descriptions of Computer-Aided Design (CAD) models in neural networks. Bézier extraction is used to build the network architecture, where Bernstein polynomials serve as the nonlinear activation functions. SplineNet can be applied in a data-free or data-driven way. In the data-free case, energy-based formulations can be naturally incorporated as loss terms, which fulfill the need of Computer-Aided Engineering (CAE) and can be accurately calculated. In particular, the Kirchhoff--Love (KL) model is adopted to solve for the mechanical behaviors of shell structures. This way, CAD and CAE can be tightly integrated in a deep neural network without the time-consuming model/data exchange process. In the data-driven case, SplineNet can be used as the trunk net of Deep Operator Networks (DeepONet) to provide interpretability. Given such a trained network and unseen input data, results can be immediately obtained without retraining the network or repeatedly performing the traditional workflow for analysis. In the end, a variety of numerical examples are studied to demonstrate the effectiveness of the proposed method, especially when real-world complex geometries are involved.

Problem

• isogeometric
• shell structures
• CAD-CAE integration
• complex geometries
• deep learning

Innovation

• isogeometric deep learning
• T-splines
• Bézier extraction
• Kirchhoff–Love shells
• CAD-CAE integration