> We develop Urania, a highly parallelized hybrid local-global optimization algorithm, sketched in Fig. 2(a). It starts from a pool of thousands of initial conditions of the UIFO, which are either entirely random initializations or augmented with solutions from different frequency ranges. Urania starts 1000 parallel local optimizations that minimize the objective function using an adapted version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. BFGS is a highly efficient gradient-descent optimizer that approximates the inverse Hessian matrix. For each local optimization, Urania chooses a target from the pool according to a Boltzmann distribution, which weights better-performing setups in the pool higher and adds a small noise to escape local minima.
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.02...