Data-driven linear solver selection and performance tuning for multiphysics simulations in porous media

Area of Science:

• Computational Science
• Numerical Analysis
• Scientific Computing

Background:

• Efficient multiphysics simulations in porous media demand optimized preconditioned iterative linear solvers.
• Selecting optimal sub-algorithms and parameters for these solvers is complex due to numerous combinations and changing simulation setups.

Purpose of the Study:

• To develop an automated algorithm for selecting and tuning preconditioned linear solvers for multiphysics simulations.
• To address the challenge of optimizing solver choices when numerous similar linear systems are solved sequentially.

Main Methods:

• A novel solver selection algorithm that collects performance data during simulations.
• Continuous updating of a machine learning model to refine the solver selection policy adaptively.
• Evaluation on time-dependent nonlinear model problems: fluid flow/heat transfer and thermo-poromechanics in porous media.

Main Results:

• The algorithm successfully selects efficient and robust solvers with minimal overhead.
• Performance is comparable to a reference policy with complete prior data access.
• Demonstrated effectiveness on coupled fluid flow/heat transfer and thermo-poromechanics simulations.

Conclusions:

• The proposed approach effectively automates solver selection and tuning for multiphysics simulations.
• Offers significant value to researchers and engineers, especially in the absence of specialized solver expertise.