用在线学习方法一击提速瞬态方程求解器，无需训练数据。
One-shot acceleration of transient PDE solvers via online-learned preconditioners
- 基于强化学习动态调整预条件子配置，实时优化求解过程。
- 在流体与磁流体力学问题上实现一击式加速，显著提升求解效率。
- 直接集成于OpenFOAM，适合需要快速模拟的工程与科研场景。
机器学习在科学计算中的数据驱动加速已成为热门方向，其中瞬态偏微分方程（PDE）的数值模拟是主要应用之一。以往方法依赖经典仿真数据进行训练，但神经网络对数据需求大且优化困难，难以在强基线面前展现明显优势。本文提出新范式：利用经典求解器自身产生的数据来加速其自身。由于瞬态PDE常需求解一系列相关线性系统，可借助带负反馈的线性求解器（如预条件共轭梯度法，PCG）输出，由老虎机算法在线学习自适应的求解器配置序列（如预条件子）。我们提出的PCGBandit方法直接部署于开源软件OpenFOAM，在一组流体与磁流体力学（MHD）问题上验证了其有效性。
原文摘要 · Abstract (English)
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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