PCGBandit: One-shot acceleration of transient PDE solvers via online-learned preconditioners
This addresses the problem of slow numerical simulations for researchers in computational science, offering a novel approach that avoids the data-hungry training of neural networks.
The paper tackles the challenge of accelerating transient PDE solvers by introducing PCGBandit, a method that uses online-learned preconditioners to achieve a one-shot speedup, demonstrating effectiveness on fluid and magnetohydrodynamics problems with OpenFOAM.
Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications. The focus thus far has been on methods that require classical simulations to train, which when combined with the data-hungriness and optimization challenges of neural networks has caused difficulties in demonstrating a convincing advantage against strong classical baselines. We consider an alternative paradigm in which the learner uses a classical solver's own data to accelerate it, enabling a one-shot speedup of the simulation. Concretely, since transient PDEs often require solving a sequence of related linear systems, the feedback from repeated calls to a linear solver such as preconditioned conjugate gradient (PCG) can be used by a bandit algorithm to online-learn an adaptive sequence of solver configurations (e.g. preconditioners). The method we develop, PCGBandit, is implemented directly on top of the popular open source software OpenFOAM, which we use to show its effectiveness on a set of fluid and magnetohydrodynamics (MHD) problems.