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 (PINNs) 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 PINN, 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 quantum PINNs,
for complex shape optimization tasks in computational fluid dynamics. By
improving the accuracy of fluid simulations in complex geometries, our research
using quantum PINNs contributes to the development of more efficient and
reliable fluid dynamics solvers.

我们提出了一种使用混合的量子物理信息神经网络的方法，模拟了三维 Y 形混合器中的层流流体，该方法结合了量子模型的表达力和 PINN 的灵活性，与纯经典神经网络相比，精度提高了 21％。