论文标题
动态系统的模型受限的切线学习方法
A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems
论文作者
论文摘要
大规模复杂动力系统的实时准确解决方案非常需要控制，优化，不确定性量化以及实用工程和科学应用，尤其是数字双胞胎应用程序中的决策。本文朝着这个方向做出了贡献，一种模型约束的切线学习（MCTANGENT）方法。 McTangent的核心是几种理想策略的协同作用：i）切线斜率学习，以利用线条方法的神经网络速度和时间准确的性质； ii）一种模型受限的方法，用于编码神经网络切线斜率与底层控制方程； iii）促进长期稳定性和准确性的顺序学习策略； iv）数据随机方法隐式强制执行神经网络切线斜率的平滑性及其对真相切线斜率的可能性，以进一步提高mctangent solutions的稳定性和准确性。提供了严格的结果来分析和证明所提出的方法是合理的。提出了有关传输方程，粘性汉堡方程和Navier-Stokes方程的几个数值结果，以研究和证明所提出的MCTANGENT学习方法的稳健性和长期准确性。
Real-time accurate solutions of large-scale complex dynamical systems are in critical need for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, especially digital twin applications. This paper contributes in this direction a model-constrained tangent slope learning (mcTangent) approach. At the heart of mcTangent is the synergy of several desirable strategies: i) a tangent slope learning to take advantage of the neural network speed and the time-accurate nature of the method of lines; ii) a model-constrained approach to encode the neural network tangent slope with the underlying governing equations; iii) sequential learning strategies to promote long-time stability and accuracy; and iv) data randomization approach to implicitly enforce the smoothness of the neural network tangent slope and its likeliness to the truth tangent slope up second order derivatives in order to further enhance the stability and accuracy of mcTangent solutions. Rigorous results are provided to analyze and justify the proposed approach. Several numerical results for the transport equation, viscous Burgers equation, and Navier-Stokes equation are presented to study and demonstrate the robustness and long-time accuracy of the proposed mcTangent learning approach.
