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

Area of Science:

• Computational Engineering
• Machine Learning
• Numerical Analysis

Background:

• Fast numerical predictions are crucial for engineering design, optimization, and uncertainty quantification.
• Existing methods like Finite Element Method (FEM) can be computationally expensive.
• Seamless integration into Computer-Aided Design (CAD) and numerical analysis workflows is needed.

Purpose of the Study:

• Introduce IGANets, a novel spline-based, physics-informed machine learning framework.
• Enable fast, accurate numerical predictions integrated with CAD and numerical analysis tools.
• Demonstrate the feasibility and generalization capability of IGANets.

Main Methods:

• Formulated IGANets in a collocation setting directly from physical models.
• Utilized spline-based, physics-informed neural networks.
• Conducted numerical experiments for Poisson equation and linear elasticity problems.
• Assessed generalization with multi-instance linear-elasticity problems (I-beam geometries).

Main Results:

• IGANets demonstrated feasibility for Poisson and linear elasticity problems.
• The framework showed generalization capability for unseen geometries and boundary conditions.
• Prediction accuracy improved with an increased number of training samples.

Conclusions:

• IGANets provide a viable approach for accelerated numerical predictions in engineering.
• The physics-informed, spline-based nature allows seamless integration into existing workflows.
• IGANets offer improved accuracy and generalization for engineering design tasks.