基于频域控制约束的物理神经网络非线性系统预测方法

Nonlinear System Prediction Method of Physical Neural Networks Based on Frequency Domain Control Constraints

针对现有物理信息神经网络利用数值模拟近似物理控制方程带来的高计算代价、边界条件限制等问题,提出一种基于频域控制约束的物理神经网络非线性系统预测方法。首先构建时序特征交替更新的非线性预测网络模型,再在频域建立基于傅里叶谱方法(FSM)的物理控制方程约束,时空数据在网络模型与频域控制约束耦合下实现无标签数据加速训练,完成系统演化学习。最后在Burgers系统上进行湍流预测验证,实验结果表明该方法可在物理规则约束下实现无标签非线性复杂建模,对比主流PINN模型及其变体,具有更快的学习速度与预测准确率。在t≤0.25 s、t≤0.5 s短时预测情况下,经前期20次训练后系统预测均方误差(MSE)相比主流基准模型同期预测,MSE降低了86%与95%,在t≤2 s长时预测情况下,经充分训练后系统预测MSE能降低80%。

To address the problems of high computational cost and boundary condition limitations associated with the existing physical information neural network using numerical simulation to approximate the physical control equations,a nonlinear system prediction method of physical neural networks based on frequency domain control constraints is proposed.Firstly,a nonlinear prediction network model with alternating updates of temporal features is constructed,followed by a physical control equation constraint based on the Fourier spectrum method(FSM)in the frequency domain,and then the spatio-temporal data are trained without labels under the coupling of the network model and the frequency domain control constraint to complete the system evolution learning.The experimental results show that the proposed method can achieve unlabeled nonlinear complex modeling under physical rule constraints,and has faster learning speed and prediction accuracy compared with the mainstream Physics Informed Neural Network(PINN)model and its variants.In the case of t≤0.25 s and t≤0.5 s short-time prediction,the Mean Square Error(MSE)of the system is reduced by 86%and 95%compared with that of the mainstream baseline model in the same period of time after 20 times of pre-training,and the MSE of the system can be reduced by 80%in the case of t≤2 s long-time prediction after sufficient training.