用神经滤波器提升神经网络对动态系统的长期预测精度。
A Novel Neural Filter to Improve Accuracy of Neural Network Models of Dynamic Systems
- 借鉴扩展卡尔曼滤波，融合物理测量与网络预测
- 在4个非线性系统上显著降低误差并稳定估计方差
- 可让训练不足的模型达到良好训练模型的精度
神经网络在建模动态系统方面应用广泛，因其能估计复杂非线性函数。然而在长期预测中，预测误差随时间发散，导致精度下降。本文提出一种神经滤波器，用于提升基于神经网络的动态系统长期状态预测精度。受扩展卡尔曼滤波启发，该方法将神经网络的状态预测与物理系统的实际测量值结合，优化状态估计。在四个非线性动力学系统上的数值实验表明，神经滤波器显著提高了预测精度，并有效约束了状态估计协方差，优于纯神经网络预测。此外，即使初始训练较差的神经网络模型，经滤波后也能达到良好训练模型的精度水平，有望降低训练成本和数据需求。
原文摘要 · Abstract (English)
The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where the prediction error diverges over time, thus degrading their accuracy. This paper presents a neural filter to enhance the accuracy of long-term state predictions of neural network-based models of dynamic systems. Motivated by the extended Kalman filter, the neural filter combines the neural network state predictions with the measurements from the physical system to improve the estimated state's accuracy. The neural filter's improvements in prediction accuracy are demonstrated through applications to four nonlinear dynamical systems. Numerical experiments show that the neural filter significantly improves prediction accuracy and bounds the state estimate covariance, outperforming the neural network predictions. Furthermore, it is also shown that the accuracy of a poorly trained neural network model can be improved to the same level as that of an adequately trained neural network model, potentially decreasing the training cost and required data to train a neural network.
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