Data-driven model order reduction with surrogate elements for transient simulations

Purpose The purpose of this study is to introduce surrogate elements for static and transient finite element simulations. These elements are designed to replace regions of several conventional solid elements with a single artificial element that possesses a reduced number of degrees of freedoms (dofs). A notable advantage of our surrogate elements is their seamless integration into standard finite element meshes. Design/methodology/approach The construction of the surrogate elements stiffness and mass matrices is achieved through an optimization process wherein displacements serve as the optimization objective. Moreover, the matrices are designed to possess properties analogous to those of standard finite elements. A particular focus is placed on ensuring that the artificial stiffness matrices are positive semi-definite. Furthermore, artificial degrees of freedom are introduced. Findings The efficacy of the proposed technique is demonstrated through its application to two different use cases. It is demonstrated that, despite being trained on examples comprising a single surrogate element, the surrogate elements can be employed multiple times within complex and practical models. The degree of accuracy achieved in these applications is noteworthy. Moreover, the proposed method is considerably faster than the fully discretized models. Originality/value The study expands the field of substructuring and model order reduction by incorporating artificial surrogate elements built by neural networks, which enables seamless integration with standard finite element analysis via positive semi-definite matrices. Furthermore, the introduction of artificial degrees of freedom, which are detached from the computational domain, is proposed. Once trained, the surrogate elements can be utilised in load and support independent scenarios.