为配备替代模型的动力系统设计一种快速时间步进策略
A fast time-stepping strategy for dynamical systems equipped with a surrogate model
AI总结：
本文提出一种结合替代模型和完整模型的加速时间步进策略，以提高复杂动力系统模拟的效率。
摘要：
复杂动力系统在许多应用中的模拟在计算上具有挑战性，由于其规模和复杂性。模型降阶、机器学习和其他类型的替代建模技术提供了更经济和简单的方式来描述这些系统的动力学，但它们是不精确的，并引入了额外的近似误差。为了克服完整复杂模型的计算困难，一方面，以及替代模型的限制，另一方面，本工作提出了一种新的加速时间步进策略，结合了两者的相关信息。该方法基于多速率无穷小通用结构加法Runge-Kutta（MRI-GARK）框架。廉价的替代模型与小时间步长相结合，以引导解轨迹，而完整模型则用大时间步长偶尔修正替代模型误差，以确保收敛。我们提供了理论误差分析和若干数值实验，以证明这种方法比仅使用完整模型或仅使用替代模型进行积分要高效得多。
英文摘要：
Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge-Kutta (MRI-GARK) framework. The inexpensive surrogate model is integrated with a small timestep to guide the solution trajectory, and the full model is treated with a large timestep to occasionally correct for the surrogate model error and ensure convergence. We provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.
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