Combinatorics

Finite element method

Topology (electrical circuits)

Mathematics

Structural engineering

Engineering optimization

Mathematical optimization

Engineering

Optimization problem

Topology optimization

Computer science

Computer Methods in Applied Mechanics and Engineering

Topology optimization is a powerful methodology for generating novel designs with a high degree of design freedom. In exchange for this attractive feature, topology optimization cannot generally avoid multimodality, which often impedes finding a satisfactory solution when dealing with strongly nonlinear optimization problems. In this study, we focus on constructing a framework that aims to indirectly solve such complex topology optimization problems. The framework is based on multifidelity topology design (MFTD), the basic concept of which is to divide solving an original topology optimization problem into two kinds of procedures, i.e., low-fidelity optimization and high-fidelity evaluation. We build the framework as a data-driven approach, where the design candidates given by solving the low-fidelity optimization problem are iteratively updated based on the idea of the evolutionary algorithm (EA). As a key procedure to realize a crossover-like operation in the high-dimensional design space, a variational autoencoder—one of the representative deep generative models—is utilized for generating a new dataset composed of various material distributions. Besides, we propose a mutation-like operation for generating novel material distributions based on reference ones in the dataset. By integrating these operations with an elitism-based selection procedure, we propose data-driven MFTD that enables gradient-free optimization even if tackling a complex optimization problem with a high degree of design freedom. We apply the proposed framework to forced convection heat transfer problems, where the low-fidelity optimization problem is formulated using a Darcy flow model, whereas the high-fidelity evaluation is conducted using a Navier–Stokes model. We first demonstrate that the obtained results from the proposed framework can achieve almost identical performance compared with that of the directly solved results in a well-known 2D laminar heat transfer problem. We then show that the proposed framework can find solutions in minimax problems of topology optimization pertaining to 3D laminar and turbulent heat transfer.

Data-driven multifidelity topology design using a deep generative model: Application to forced convection heat transfer problems