Self-similar blow up profiles for fluids via physics-informed neural networks

In this talk I will explain a new numerical framework, employing physics-informed neural networks, to find a smooth self-similar solution (or asymptotically self-similar solution) for different equations in fluid dynamics, such as Euler or Boussinesq. The new numerical framework is shown to be both robust and readily adaptable to several situations. Joint work with Tristan Buckmaster, Gonzalo Cao-Labora, Ching-Yao Lai and Yongji Wang.