Quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes

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.