
Accelerating Isogeometric Analysis of Solids with Neural Networks
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Solids are typically created using boundary representation modeling techniques in Computer Aided Design (CAD) and Isogeometric Analysis (IGA) aims to leverage this representation throughout the entire analysis process. This work explores data-driven techniques to accelerate isogeometric analysis of solids and enhance the efficiency of optimization workflows. We consider linear elasticity problems with solutions for different discretization configurations, where the position of the control points is parameterized [1]. In order to reduce the dimension of the problem, we use singular value decomposition (SVD) in combination with neural networks [2]. The accuracy is evaluated using parameters that vary the position of the control points and are different than the ones used for training the network. Furthermore, we employ this approach to minimize a given objective function in order to obtain fast and accurate predictions within optimization workflows. We investigate the applicability of the approach to isogeometric and scaled boundary discretizations. The latter are a combination of IGA with the scaled boundary finite element method to describe the entire solid. Here, the boundary surfaces are related to a scaling center in order to partition the solid into sections, which are then described by tri-variate B-Splines [3]. We employ several parametrizations and numerical examples that show the accuracy and computational speedup of the presented approach, thus highlighting its potential to enhance analysis and optimization tasks. REFERENCES [1] M. Chasapi, P. Antolin, A. Buffa: Reduced order modeling of non-affine problems on parameterized NURBS multi-patch geometries, Lecture Notes in Computational Science and Engineering (2024), 151: 67-87. [2] J.S. Hesthaven, S. Ubbiali: Non-intrusive reduced order modeling of nonlinear problems using neural networks, Journal of Computational Physics (2018), 363: 55-78. [3] M. Chasapi, L. Mester, B. Simeon, S. Klinkel: Isogeometric analysis of 3D solids in boundary representation for problems in nonlinear solid mechanics and structural dynamics, Int. J. Numer. Meth. Engng. (2021), 123: 1228–1252.