Hybrid Training of Physics-Informed Neural Networks with Approximate Supervision

A major bottleneck in multidisciplinary design optimization (MDO) is its high computational cost, with large-scale problems often requiring hours or days to complete. To address this issue, engineers turn to low-fidelity models or data-driven surrogate models such as neural networks. However, while these approaches significantly reduce runtime, they often sacrifice accuracy, which can impact the quality of optimization results. Physics-informed neural networks (PINNs) offer a promising middle ground by embedding physical governing equations directly into the training process, enabling both quick evaluation and high accuracy. Despite their potential, traditional PINNs often converge to non-physical solutions, limiting their use in real-world applications. Thus, many of the applications of PINNs in existing literature are limited to academic problems. In this paper, we demonstrate accurate flow field predictions on a three-dimensional domain around a complex aircraft geometry using PINNs, achieving a nondimensional PDE residual of less than 5e-3 and an average surface tangency error of less than 2°. We avoid common failure modes associated with PINNs by leveraging inexpensive approximate data to help guide the network to a physical solution, qualitatively matching the reference solution. We also improve convergence speed compared to standard neural networks by encoding geometric information in the neural network architecture. We believe this demonstration on a practical application takes a step towards the use of PINN-based models in MDO workflows.