An Ising Machine Formulation for Design Updates in Topology Optimization of Flow Channels

TL;DR

This work presents a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels and shows that the proposed update strategy can accelerate the topology optimization process while producing comparable designs.

Abstract

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.

Figures (8)

• Figure 1: The problem setting of the diffuser problem (left) and the double pipe problem (right).
• Figure 2: Diffuser problem: the number of elements $k$ with inconsistent values of $\phi^{k}$ and $\chi^{k}_{f}$ for different values of $\lambda_{\text{char}}$.
• Figure 3: Diffuser problem: effect of the regularization term on the level-set function $\phi^{k}$ (top) and the characteristic function $\chi^{k}_{f}$ (bottom) through different values of $\lambda_{\text{reg}}$, increasing from left to right.
• Figure 4: Diffuser problem: final designs for different values of $\lambda_{\text{dis}}$ (rows) and $\lambda_{\text{reg}}$ (columns).
• Figure 5: Diffuser problem: final designs for the classical approach (left) and the annealing approach (right).