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.

翻译：拓扑优化是计算工程中的一项重要工具，例如用于改进流道的设计与效率。同时，包括数字或量子退火器在内的伊辛机已被用作组合优化问题的高效求解器。除了组合优化，近期研究通过定制相应的问题公式，展示了其在其他工程任务中的适用性。在本研究中，我们提出了一种新颖的伊辛机公式，用于在拓扑优化过程中计算设计更新，其目标是最小化流道中的耗散能量。我们探索了该方法在提高优化过程效率与性能方面的潜力。为此，我们通过实验研究了新公式中各种因素的影响。此外，我们将其与一种经典方法进行比较，分别以优化步骤数和目标函数的最终值作为优化时间强度和所得设计性能的指标。我们的研究结果表明，所提出的更新策略能够加速拓扑优化过程，同时产生具有可比性的设计。然而，该方法往往探索性较弱，可能导致设计性能较低。这些结果凸显了将伊辛公式融入优化任务的潜力，但也揭示了其在迭代优化过程中用于计算设计更新时的局限性。总之，本研究为拓扑优化中的设计更新提供了一种高效替代方案，并增进了对伊辛机公式在工程优化中整合应用的理解。