Discovering new solutions to century-old problems in fluid dynamics

Developed a new AI-driven method for discovering unstable singularities in fluid dynamics equations. This method utilizes Physics-Informed Neural Networks (PINNs) trained to satisfy physical laws, achieving high precision and enabling the systematic identification of new singularity families in the Euler, Incompressible Porous Media (IPM), and Boussinesq equations. The research also identified a pattern in the blow-up speed (lambda) related to the order of instability, suggesting further undiscovered solutions.