Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

This lecture by the instructor focuses on explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems. The content covers the statement of optimization and sampling problems, applications in machine learning and imaging inverse problems, gradient flow, Langevin dynamics, speed of convergence, numerical discretisation, quadratic minimisation, and the use of stabilised methods in optimization and sampling. The lecture also delves into the implementation, complexity, and cost reduction of these methods, as well as their use in optimisation and sampling for imaging inverse problems. The presentation concludes with discussions on stiffness through smoothing, the behaviour of the auto-correlation function, and future work in the field.