From machine-learned preconditioners to control-oriented models

A good understanding of your problem is essential when applying machine learning tools. Various types of problems result in linear systems with their own kind of structure, which can be exploited by the right machine learning tool. We know this, because our team has developed cutting-edge tools such as:

• Data-driven (and relatively cheap) preconditioners (PreconNet), applied to plasma simulations but applicable to any problem that gives rise to a linear system of equations.
• Surrogate models for tokamak turbulunce (QLKNN).
• Machine-learned solver selection for Finite Element (FEM) codes, capable of selecting between various solvers during time stepping to decrease total solve time.
• Surrogate models for solution prediction in Finite Element codes, providing initial guesses to an iterative solver to decrease the required solve time.
• Parameter optimization for a specific solver and problem, reducing overall solve time.