PCGBandit: One-shot acceleration of transient PDE solvers via online-learned preconditioners

• URL: http://arxiv.org/abs/2509.08765v2
• Date: Fri, 12 Sep 2025 03:49:57 GMT
• Title: PCGBandit: One-shot acceleration of transient PDE solvers via online-learned preconditioners
• Authors: Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen,
• Abstract summary: We develop an algorithm that accelerates numerical simulation of transient partial differential equations (PDEs) using a classical solver's own data.<n>The PCGBandit algorithm is implemented directly on top of the popular open source software OpenFOAM.
• Score: 8.58199539913211
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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