Dynamic Linear Solver Selection for Transient Simulations Using Machine Learning on Distributed Systems

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 the model moving closer to a state of equilibrium where the linear systems are easier to solve. Machine learning algorithms provide the ability to dynamically select the preconditioned linear solver for each linear system produced by a simulation. We can generate databases by computing attributes for each linear system, physical attributes for the transient simulation, computational attributes, and running times for a set of preconditioned solvers on each linear system. Machine learning algorithms can then use these databases to generate classifiers capable of dynamically selecting a preconditioned solver for each linear system given a set of attributes. This allows us to quickly and accurately compute each transient simulation using different preconditioned solvers throughout the simulation. This also provides the potential to produce speedups in comparison with using a single preconditioned solver for an entire transient simulation.