Benchmarking Quantum-Assisted PINN (QA-PINN) for Computational Fluid Dynamics

Physics-Informed Neural Network (PINN) is a powerful method in computer-aided engineering (CAE), especially for design space exploration studies (like surrogate modeling and design of experiments), that combines deep learning with physics-based modeling. Though PINN is in a nascent stage, its success hinges on two key factors - generalizability and training efficiency. One common aspect of these factors is trainable parameters. The goal of this study is to improve these two factors by the introduction of Quantum Machine Learning in a classical PINN framework. This study proposes a Quantum-Assisted PINN (QA-PINN) to reduce the trainable parameters while maintaining accuracy. The study utilized a standard forward problem of simulating partial differential equations (PDEs) from the field of Computational Fluid Dynamics (CFD), a well-understood area with classical PINN. A comparative analysis was performed between QA-PINN, equivalent classical vanilla PINN (c-PINN), and state-of-the-art classical PINN - Globally Adaptive Activation Function PINN (GAAF-PINN). All methods were benchmarked against the ground-truth analytical solution for 1D Burger's equation. The analysis is conducted for 3, 4, and 5-qubit QA-PINN architectures. In comparison to c-PINN and GAAF-PINN, 4 and 5-qubit QA-PINN is shown to reduce the number of trainable parameters of the network by 20%, and while maintaining the accuracy. The reduced number of trainable parameters indicates the reduced complexity of the model and the reduced risk of overfitting, making it more generalizable. Thus, the proposed approach can have a significant impact on PINNs enhancing generalization and improving training efficiency for deploying the model for real-world applications.