Dynamic Linear Solver Selection for Transient Simulations Using Multi-label Classifiers

Many transient simulations spend a significant portion of the overall runtime solving a linear system. A wide variety of preconditioned linear solvers have been developed to quickly and accurately solve different types of linear systems, each having options to customize the preconditioned solver for a given linear system. Transient simulations may produce significantly different linear systems as the simulation progresses due to special events occurring that make the linear systems more difficult to solve or move the model closer to a state of equilibrium with easier to solve linear systems. Machine learning algorithms provide the ability to dynamically select the preconditioned linear solver for each linear system produced by a simulation. We test both single-label and multi-label classifiers, demonstrating that multi-label classifiers achieve the best performance due to associating multiple fast linear solvers with each tested linear system. For more difficult simulations, these classifiers produce significant speedups, while for less difficult simulations these classifiers achieve performance similar to the fastest single preconditioned linear solvers. We test classifiers generated using limited attribute sets, demonstrating that we can minimize overhead while still obtaining fast, accurate simulations.