## 1 Introduction  
As the size and complexity of numerical models used in structural analysis and design are continuously augmenting and there is no analogous increase in the available computing power, the advantages gained through the exploitation of soft computing techniques are often investigated. In the case of gradient-based optimization algorithms, where sensitivity analysis plays a significant role during the search process, up to 90% of the computations are devoted to the solution of the equilibrium equations:  
\[P=K\times\ U \tag{1}\]  
whereas the respective percentage exceeds 97% in metaheuristic search algorithms. In Equation (1), \(U\) and \(P\) denote the displacement and loading vectors, respectively, and \(K\) refers to the stiffness matrix of the structural system. Therefore, the solution of real-world, large-scale, complex structural optimization problems is a computationally demanding undertaking.  
Structural optimization problems can generally be distinguished into three categories: sizing, shape and topology optimization [1, 2, 3]. The latter aims to identify the optimal topological arrangement of the material over the design domain of a structural system, for a given set of load and support conditions. In principle, topology optimization supersedes sizing and shape optimization, in the sense that its output is also optimal with respect to sizing and shape criteria. The application of such approaches enables the establishment of structural systems that are virtually optimal in shape, thus providing an invaluable guide throughout the conceptual design phase [4; 5].  
Over the past decade, research on modern soft computing techniques drew significant attention [6], leading to the development of new methods able to handle large amounts of data and extremely complex problem definitions. The focus of the present study is on the application of soft computing methods in the fields of optimal analysis and design of structures, wherein recently there is a growing interest for exploiting deep learning techniques to accelerate topology optimization procedures. A detailed state-of-the-art review, along with a topology optimization via neural reparameterization framework, can be found in the work of [PERSON] et al. [7].  
Some of the most computationally demanding problems in structural optimization are those that involve several solutions of the equilibrium equation (Equation (1)), as factorizing the stiffness matrix is time- and resource-consuming. To overcome this limitation, it is necessitated to resort to techniques that reduce the order of the stiffness matrix, minimize the necessary iterations of the search process or achieve a combination of these. This work aims to achieve both objectives, by virtue of establishing a novel model order reduction scheme and minimizing the required number of iterations for the topology optimization problem solution. The proposed scheme is labeled DLMU, which stands for \"Deep Learning-based Model Upgrading\", and is founded on the idea of using deep learning to extrapolate results of small- to large-scale models without compromising the solution quality.  
The paper proceeds with providing an overview of deep learning procedures in Section 2, followed by a description of the accelerated topology optimization concept in Section 3. Subsequently, in Section 4 the proposed Deep Learning-based Model Upgrading (DLMU) scheme is described in detail, and Section 5 contains the results of the numerical tests performed to assess its efficiency in comparison with other acceleration techniques of the solution process of the topology optimization problem.