Exploration of Finite Basis Physics-Informed Neural Networks for predicting droplet dynamics in aircraft icing problems

This thesis explores the use of an innovative machine learning algorithm for the
prediction of the droplet dynamics, an important and often time-consuming step
in in-flight icing simulations. In-flight icing poses a serious risk to the maneuverability and safety of aircraft, manifesting itself when passing through clouds containing supercooled water droplets, which freeze on impact. Having accurate predictions of droplet impingement and ice accretion is highly relevant to aircraft research and design and ice protection system design. The study evaluates the application of finite basis physics informed neural networks (FBPINNs), inspired by the finite element method. FBPINNs are a domain decomposition-based extension of physics-informed neural networks (PINNs), in which the computational domain is subdivided into overlapping subdomains, each assigned to a local neural network. The networks are trained as function approximators by minimizing the residuals of the governing partial differential equations. The global solution emerges from the combination of these locally trained networks, enabling efficient and scalable approximation over the full domain. The main objective is to adapt FBPINNs to predict the velocity field of the droplets and the local liquid water content in a 2D field. During training, flow field data required for the governing equations was obtained from ANSYS Fluent simulations. Model performance was evaluated on two benchmark cases in which the airflow was perturbed by a mass and a momentum source, respectively. For evaluation, synthetic ground truth data was provided by ANSYS DROP3D (FENSAP-ICE module), serving as a reference for the physical
behavior of the system.

A sensitivity analysis was conducted to assess the impact of the number of subdomains, extent of subdomain overlap, number of the governing equation sample points, network architecture and droplet size. The most influential parameter proved to be the number of subdomains, which improved performance without increasing computational costs. A critical threshold of the sample points was also observed, below which performance drops signiffcantly. The overlap helps to reduce background noise of the solution, improves accuracy for low-intensity phenomena and interacts positively with the number of subdomains, reducing data requirements and increasing efficiency. This work presents an initial exploration of the use of FBPINNs in droplet trajectory calculation for icing simulation, highlighting their potential and advantages in
the context of physics informed neural networks (PINNs).