Bridging the gap between isogeometric analysis and deep operator learning

Matthias Möller (TU Delft)

Abstract. Isogeometric Analysis (IgA) introduced by Hughes et al. in 2005 has revived the vision of design-through-analysis (DTA) originally proposed by Augustitus et al. in 1977. DTA means the fully virtual creation, analysis and optimization of engineering designs, which requires bidirectional exchange of data between computer-aided design (CAD) and engineering analysis (CAE) tools.
While IgA targets at bridging the gap between CAD and CAE through the use of spline basis functions throughout the entire process, the full potential of DTA is hold back by high computational costs of simulation-based analysis tools that hinder truly interactive DTA workflows.
In this presentation we will briefly review the mathematical basics of IgA and present a novel approach – IgANets – that integrates the concept of deep operator learning into the isogeometric framework. In particular, we show that IgANets can be interpreted as a network-based variant of least-squares collocation IgA (Lin et al. 2020), thereby inheriting its consistency and convergence properties. We will moreover present a prototype of an interactive VR workflow which allows the collaborative creation and analysis of designs.