Both nonlinear integrable and non-integrable systems can exhibit complex solutions, such as solitons or even singularities. The most notable open problem is that of hydrodynamics, i.e. the Euler and Navier–Stokes equations. This project aims to apply new machine learning techniques to analyse complex physical systems described by partial differential equations (PDEs), with a focus on the nonlinear Schrödinger class of models. Specifically, the goal is to investigate whether Physics Informed Neural Networks (PINNs) can capture the formation of singular solutions and possibly suggest unknown behaviour. This internship is a collaboration between LADHYX at Polytechnique and LISN at Paris-Saclay.