A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems
A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems
复制标题
一种动态系统的模型约束切线斜率学习方法
DOI：
10.1080/10618562.2022.2146677
复制
发表时间：
2022-08
影响因子：
1.3
通讯作者：
Hai V. Nguyen;T. Bui-Thanh
中科院分区：
文献类型：
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作者：
Hai V. Nguyen;T. Bui-Thanh
在实际工程和科学应用中，特别是数字孪生应用中，对大型复杂动力系统的控制、优化、不确定性量化和决策都迫切需要实时精确的解决方案。本文在这个方向上的模型约束切线斜率学习（mcTangent）的方法。mcTangent的核心是几种理想策略的协同作用：（i）切线斜率学习，以利用神经网络的速度和线方法的时间精确性;（ii）模型约束方法，以编码神经网络切线斜率与底层控制方程;（iii）顺序学习策略，以提高长期稳定性和准确性;以及（iv）数据随机化方法，以隐含地加强神经网络切线斜率的平滑性及其与二阶导数上的真值切线斜率的相似性，以便进一步增强mcTangent解决方案的稳定性和准确性。严格的结果提供分析和证明所提出的方法。输运方程，粘性Burgers方程，和Navier-Stokes方程的数值结果研究和证明所提出的mcTangent学习方法的鲁棒性和长期精度。
Real-time accurate solutions of large-scale complex dynamical systems are in critical need for control, optimisation, 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 randomisation 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 analyse and justify the proposed approach. Several numerical results for 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.