Computer simulations coupled with theoretical methods from statistical mechanics are a key tool to predict and explain experimental results. In the last 20 years, theory made important steps towards a deeper understanding of how matter transforms: piece by piece, a general framework is emerging, able to explain phase transitions, chemical reactions, and the fascinating operations of biomolecular machines. The basic ingredients are molecular dynamics (MD) simulations and stochastic processes (Langevin and Fokker-Planck equations) coupled with out-of-equilibrium thermodynamics. Our research group at Sorbonne University recently invented new efficient computational approaches based on rigorous mathematical results, completing several pilot projects (see https://sites.google.com/site/fabiopietrucci/Home/papers ). The internship will develop new ways to access important physical information: free-energy barriers and kinetic rates will be estimated using non-conventional methods, and new types of loss function – the key quantity in machine learning optimizations – will be explored, based on physical variational principles, to identify optimal reaction coordinates based on scientific criteria and not solely on data science. The internship could be the first step of a PhD thesis, in collaboration with world leaders in the field at the universities of Amsterdam and Vienna, and at SISSA in Trieste.