DL-SCALE: a novel deep learning-based model order upscaling scheme for solving topology optimization problems

The main scope of this study is to propose a novel methodology aiming at enhancing the computational efficiency of the approaches used for solving structural topology optimization (STO) problems. The methodology is based on machine learning combined with the idea of using multiple finite element (FE) models of reduced order. The capability of deep belief networks (DBNs) in discovering multiple representational levels of data nonlinearity in pattern recognition problems recently triggered the development of the DLTOP methodology by the authors Kallioras et al. (Struct Multidiscip Optim, 2020, 10.1007/s00158-020-02545-z), that is based on DBNs and the solid isotropic material with penalization (SIMP) approach. In this study, a FE model order upgrading scheme integrated with the DLTOP methodology is proposed for accelerating further the SIMP-based solution procedure of the STO problems with no scalability limitations, labeled as DL-SCALE. The framework of DL-SCALE is based on a combined implementation of DBNs and SIMP into a sequentially implemented "model-optimize-and-order-upgrade" scheme. DL-SCALE efficiency is validated over several benchmark topology optimization test-examples. The results obtained for the test-examples clearly prove its computational advantages; the computing time is reduced by almost one order of magnitude while the corresponding reduction in terms of iterations is more than one order of magnitude compared to the ones originally required by SIMP, without any loss with respect to objective function value. It is also concluded from the results obtained that the proposed methodology can escalate to various finite element mesh discretizations, while optimized layout information transfer is possible, contributing also in accelerating further the STO procedure.