Radial basis function interpolation of fields resulting from nonlinear simulations

• Published in: Engineering with computers Vol. 40; no. 1; pp. 129 - 145
• Main Authors: de Gooijer, Boukje M., Havinga, Jos, Geijselaers, Hubert J. M., van den Boogaard, Anton H.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2024; Springer Nature B.V
• Subjects: CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Control algorithms; Criteria; Decomposition; Interpolation; Math. Applications in Chemistry; Mathematical and Computational Engineering; Metal forming; Original Article; Radial basis function; Reduced order models; Simulation; Singular value decomposition; Systems Theory; Proper orthogonal decomposition; Truncation criterion; Surrogate model; Metamodel; Multiphysical field
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-022-01778-4

Three approaches for construction of a surrogate model of a result field consisting of multiple physical quantities are presented. The first approach uses direct interpolation of the result space on the input space. In the second and third approaches a Singular Value Decomposition is used to reduce the model size. In the reduced order surrogate models, the amplitudes corresponding to the different basis vectors are interpolated. A quality measure that takes into account different physical parts of the result field is defined. As the quality measure is very cheap to evaluate, it can be used to efficiently optimize hyperparameters of all surrogate models. Based on the quality measure, a criterion is proposed to choose the number of basis vectors for the reduced order models. The performance of the surrogate models resulting from the three different approaches is compared using the quality measure based on a validation set. It is found that the novel criterion can effectively be used to select the number of basis vectors. The choice of construction method significantly influences the quality of the surrogate model.