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arXiv 1808.04258cs.LGphysics.comp-phstat.ML
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带记忆的模型降阶与动力系统的机器学习

Model Reduction with Memory and the Machine Learning of Dynamical Systems

Princeton University(普林斯顿大学);Southern University of Science and Technology(南方科技大学);Beijing Institute of Big Data Research(北京大数据研究院)

Chao Ma, Jianchun Wang, Weinan E

摘要:

著名的Mori-Zwanzig理论告诉我们,模型归约导致记忆效应。很长一段时间以来,准确有效地对记忆效应进行建模一直是开发良好的简化模型的重要但几乎不可能的任务。在这项工作中,我们探索了递归神经网络和Mori-Zwanzig形式主义之间的自然类比,以建立一种系统的方法来开发具有记忆的简化模型。提出并比较了两种训练模型--直接训练模型和动态耦合训练模型。我们将这些方法应用于Kuramoto-Sivashinsky方程和Navier-Stokes方程。数值实验表明,该方法可以产生具有良好的短期预测和长期统计性能的约简模型。

英文摘要:

The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced model. In this work, we explore a natural analogy between recurrent neural networks and the Mori-Zwanzig formalism to establish a systematic approach for developing reduced models with memory. Two training models-a direct training model and a dynamically coupled training model-are proposed and compared. We apply these methods to the Kuramoto-Sivashinsky equation and the Navier-Stokes equation. Numerical experiments show that the proposed method can produce reduced model with good performance on both short-term prediction and long-term statistical properties.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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