Shock wave prediction in transonic flow fields using domain-informed probabilistic deep learning

Transonic flow fields are marked by shock waves of varying strength and location and are crucial for the aerodynamic design and optimization of high-speed transport aircraft. While deep learning methods offer the potential for predicting these fields, their deterministic outputs often lack predictive uncertainty. Moreover, their accuracy, especially near critical shock regions, needs better quantification. In this paper, we introduce a domain-informed probabilistic (DIP) deep learning framework tailored for predicting transonic flow fields with shock waves called DIP-ShockNet. This methodology utilizes Monte Carlo dropout to estimate predictive uncertainty and enhances flow-field predictions near the wall region by employing the inverse wall distance function-based input representation of the aerodynamic flow field. The obtained results are benchmarked against the signed distance function and the geometric mask input representations. The proposed framework further improves prediction accuracy in shock wave areas using a domain-informed loss function. To quantify the accuracy of our shock wave predictions, we developed metrics to assess errors in shock wave strength and location, achieving errors of 6.4% and 1%, respectively. Assessing the generalizability of our method, we tested it on different training sample sizes and compared it against the proper orthogonal decomposition (POD)-based reduced-order model (ROM). Our results indicate that DIP-ShockNet outperforms POD-ROM by 60% in predicting the complete transonic flow field.