Machine learning for prediction with missing dynamics
Machine learning for prediction with missing dynamics
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DOI：
10.1016/j.jcp.2020.109922
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发表时间：
2021-01-12
影响因子：
4.1
通讯作者：
Yang, Haizhao
中科院分区：
文献类型：
--
作者：
Harlim, John;Jiang, Shixiao W.;Yang, Haizhao
本文提出了一个使用可用数据和机器学习技术恢复丢失的动力系统的通用框架。所提出的框架将预测问题重新表述为监督学习问题，以近似一个映射，该映射将已解决的和可识别的未解决变量的记忆与已解决的动态中缺失的组件相结合。我们通过在有限时间内解析变量的强收敛误差界限以及对各个科学领域的原型模型的数值测试来证明所提出的框架的有效性。其中包括具有多尺度相互作用的 57 模正压应力模型，模拟在大气中观察到的阻塞和非阻塞模式；非线性薛定谔方程，在光学和玻色爱因斯坦凝聚等物理领域有许多应用；Kuramoto-Sivashinsky 方程，时空混沌模式形成模拟等离子体中的俘获离子模式和反应扩散系统中的相动力学。虽然许多机器学习技术可用于验证所提出的框架，但我们发现循环神经网络在恢复已解析组件的轨迹以及平衡单点和两点统计方面优于核回归方法。这种出色的性能表明循环神经网络是恢复涉及高维函数近似的缺失动态的有效工具。 (c) 2020 Elsevier Inc. 保留所有权利。
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. We demonstrate the effectiveness of the proposed framework with a strong convergence error bound of the resolved variables up to finite time and numerical tests on prototypical models in various scientific domains. These include the 57-mode barotropic stress models with multiscale interactions that mimic the blocked and unblocked patterns observed in the atmosphere, the nonlinear Schrodinger equation which found many applications in physics such as optics and Bose-Einstein-Condense, the Kuramoto-Sivashinsky equation which spatiotemporal chaotic pattern formation models trapped-ion modes in plasma and phase dynamics in reaction-diffusion systems. While many machine learning techniques can be used to validate the proposed framework, we found that recurrent neural networks outperform kernel regression methods in terms of recovering the trajectory of the resolved components and the equilibrium one-point and two-point statistics. This superb performance suggests that a recurrent neural network is an effective tool for recovering the missing dynamics that involves approximation of highdimensional functions. (c) 2020 Elsevier Inc. All rights reserved.