基于物理信息机器学习的复杂系统长时间演化分析

Long term evolution analysis of complex systems based on physics-informed machine learning

中文关键词  物理信息神经网络  系统演化分析  非线性系统  预测分析

英文关键词  physics-informed neural networks  system evolution analysis  nonlinear systems  predictive analytics

中文摘要

      物理信息神经网络(PINN)能够将物理信息用于数值预测中, 是机器学习在非线性偏微分方程数值解中一种有前途的应用. 但是原始PINN方法在复杂非线性系统预测和长时间范围稳定准确预测方面存在固有缺陷. 为了能够利用PINN方法长期有效预测飞行器的复杂非线性偏微分运动学方程, 本文对原始PINN进行改进, 提出了一种新的自适应PINN方法. 该方法将系统长时域积分分解为具有不同初始状态的短时域, 通过采集随机初始条件的短时域偏微分方程数值解作为训练数据, 使该方法具有良好的泛化性, 以对复杂系统进行有效且稳定地长时间演化预测. 此外, 该方法通过构建自适应权重, 强迫算法专注于系统中的复杂/求解困难区域, 以解决原始PINN方法在处理复杂系统时网络梯度消失的问题, 提高PINN方法对复杂非线性偏微分方程的预测精度. 最后, 将提出的方法应用在飞行器的复杂非线性偏微分运动学方程长周期演化分析上, 以验证本算法的有效性.

英文摘要

      Physics-informed neural networks (PINN) can use physical information in numerical prediction, which is a promising application of machine learning in numerical solutions of nonlinear partial differential equations (PDEs). However, the original PINN method has inherent defects in the prediction of complex nonlinear systems and the stable and accurate prediction of long-term range. To make the PINN method to effectively predict the complex nonlinear PDEs for a long time, the PINN is improved and a new adaptive PINN method is proposed. This method decomposes the long time-domain system integral into short-term with different initial states. By collecting the numerical solution of nonlinear PDEs in short time domain with random initial conditions as training data, so that the method has good generalization, and can effectively predict the long-term evolution of complex systems. In addition, the proposed method establishes adaptive weights to automatically learn which regions of the solution are difficult, and force to focus on these regions, so as to solve the problem that the network gradient disappears when the original PINN method deals with complex systems, and improve the prediction accuracy of PINN method for complex nonlinear PDEs. Finally, the proposed method is applied to the long-period evolution analysis of complex nonlinear partial differential kinematics equations of aircrafts to verify the algorithm effectiveness.