NLS on the Lumpy Torus
Recently, I’ve found a fascinating line of work directed at advancing computational fluid dynamics using machine-learned preconditioners to speed up convergence in linear iterative solvers. In fact, the number of steps until convergence influences the performance bound of many classical optimization algorithms. Machine learning helps us to trade a cheap, data-driven approximation for fewer, costly optimization steps in the endgame of convergence. Given this context, I’ve been revisiting my studies on numerical PDE like the Nonlinear Schrodinger Equation (NLS) and here I’ll share some of the background work I took part in during the Summer of 2012....