Autonomous Linear Solver Control to Improve Performance of Simulations

Linear solvers account for among the largest portion of runtime in most kinds of numerical simulation applications. This also holds for reservoir simulations. Thus, efficient linear solvers methods such as System-AMG are a key to the successful application of reservoir simulations. It has been demonstrated earlier how different building blocks of multigrid can be combined to solver strategies that are bespoke to the application with certain kinds of simulations, such as Black-Oil, thermal or coupled geomechanics. These methods, however, still comprise a lot of options for a fine-grained control. An optimal setting of detailed parameters is a rather volatile trade-off between robustness and computational efficiency. It is determined by individual properties of a particular simulation, computing environment and accuracy requirements. That is, while an efficiently designed overall solver strategy already significantly accelerates a simulation, quite some further potential for optimization remains in many cases. This, however, is hardly exploitable manually in all details. Instead, we are proposing an autonomous control mechanism that can select parameters and methods individually. We use methods of machine learning via genetic algorithms, as it has been done earlier also in other applications. In our control mechanism, however, we combine this with a tree-based approach to limit the parameter optimization to search spaces that are considered reasonable in advance. This reduces the learning efforts. Surrogate-based techniques allow for transferring results from previous, possibly different runs to further guide the learning process. A deep integration in the solver method allows for accessing all relevant data for decision and learning processes and helps to reduce overhead costs. It also allows for reducing the number of solver setups within a simulation run and guarantees robustness by quickly reacting to convergence break-downs. We will demonstrate the benefits that such a control mechanism can provide in reservoir simulations and beyond. And we will discuss aspects of reproducibility of results.