DL-Scale: Deep Learning for model upgrading in topology optimization

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Topology optimization is used for defining the optimal arrangement of material within a specific domain with respect to transferring specific loads to predetermined supports in the best possible way. Deep learning techniques have achieved significant results in computer vision [1], natural language processing [1], big-data management [2], etc. On the contrary, not much work can be found in utilizing deep learning methods in structural engineering. In the current work, DL-Scale, a methodology based on a combination of a deep learning method along with a topology optimization method is presented, aiming in minimizing topology optimization computational loads and improving the usability of structural topology optimization. One of the most established methods in topology optimization is the Solid Isotropic Material with Penalization (SIMP) [2]. While the quality of results of SIMP is extremely high, it is also notable that it is a computationally heavy method, especially when dealing with fine discretized meshes. Deep Belief Networks (DBN) are probabilistic generative models which are formulated by sequentially connecting Restricted Boltzmann Machines (RBM) [3]. DBNs have been successfully applied is a series of problems by taking advantage of their ability to detect higher order correlations in large databases. In the current work a new methodology is proposed where a DBN is used along with SIMP in an iterative manner for vastly reducing the computational loads of fine-discretized meshes in topology optimization through model upgrading. This is achieved by training the DBN in finding hidden patterns and correlations between initial densities of finite elements produced by SIMP and the final density per element that SIMP proposes. The network is trained once on a typical topology optimization reference problem and is tested against several known to literature problems. For applying the methodology in a specific problem with dense meshing, a number of identical sub-problems are created with significantly less dense meshes and are handled sequentially. The generated sub-models are identical to the original one in terms of loading conditions, support conditions, etc. It is proven in all test cases examined and presented that the above-mentioned model-upgrading methodology manages to minimize the computational load of topology optimization as the iterations that SIMP needs to perform on a dense meshed model are vastly reduced.