Finding the distribution of the velocities and pressures of a fluid (by solving the Navier-Stokes equations) is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and the design of pipeline systems. With existing solvers, such as OpenFOAM and Ansys, simulations of fluid dynamics in intricate geometries are computationally expensive and require re-simulation whenever the geometric parameters or the initial and boundary conditions are altered. Physics-informed neural networks are a promising tool for simulating fluid flows in complex geometries, as they can adapt to changes in the geometry and mesh definitions, allowing for generalization across different shapes. We present a hybrid quantum physics-informed neural network that simulates laminar fluid flows in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a physics-informed neural network, resulting in a 21% higher accuracy compared to a purely classical neural network. Our findings highlight the potential of machine learning approaches, and in particular hybrid quantum physics-informed neural network, for complex shape optimization tasks in computational fluid dynamics. By improving the accuracy of fluid simulations in complex geometries, our research using hybrid quantum models contributes to the development of more efficient and reliable fluid dynamics solvers.

翻译：求解流体速度与压力分布（通过纳维-斯托克斯方程）是化工、能源、制药行业以及机械工程与管道系统设计中的核心任务。现有求解器（如OpenFOAM和Ansys）在对复杂几何结构进行流体动力学模拟时计算成本高昂，且每当几何参数或初始条件与边界条件发生变化时需重新模拟。物理信息神经网络作为复杂几何中流体流动模拟的前沿工具，能适应几何结构与网格定义的变化，实现不同形状间的泛化。我们提出一种混合量子物理信息神经网络，可模拟三维Y型混合器中的层流流动。该方法将量子模型的强大表达能力与物理信息神经网络的灵活性相结合，相比纯经典神经网络实现了21%的精度提升。研究结果凸显了机器学习方法（特别是混合量子物理信息神经网络）在计算流体动力学复杂形状优化任务中的潜力。通过提升复杂几何中流体模拟的精度，本工作将混合量子模型应用于流体动力学求解器的改进，为开发更高效可靠的流体动力学求解器作出贡献。