RS-Net: A Dynamic Weight Hybrid Model Integrating SDE and ConvLSTM for Stochastic Signal Processing

Abstract

This paper proposes an adaptive weight-driven stochastic differential-neural hybrid model (RS-Net), designed to address the challenge of dynamically integrating mathematical models and neural networks in modeling non-stationary random signals. RS-Net employs a dynamic weight module (DWM) to adjust the contribution ratio of stochastic differential equations (SDEs) and convolutional LSTMs (ConvLSTMs) in real time based on the residual error. The modular pipeline of RS-Net includes a hybrid architecture of SDE and ConvLSTM, with the DWM serving as the core innovation. By designing a dynamic weight module (DWM), the model can adjust the contribution ratio of the stochastic differential equation (SDE) and the convolutional LSTM online according to the real-time residual (mean absolute value 0.041±0.012). In the NASA turbine vibration signal (SNR=3dB), the RS-Net denoised the SNR to 18.7dB, which is 4.2dB higher than the LSTM, and the RMSE is reduced by 37.4%; in the S&P 500 volatility prediction, the MAPE is only 2.13%, which is 27.5% better than the fixed weight model. In particular, in the non-stationary section of the signal (such as sudden failure), the dynamic weight mechanism makes the model error drop by 58%, verifying its robustness to timevarying characteristics. 100 Monte Carlo experiments show that the RS-Net weight fluctuation variance is only 0.034, significantly lower than the fixed weight of 0.412, proving the stability of the adaptive strategy. The experimental results show that RS-Net breaks through the static limitations of traditional hybrid methods through deep coupling of data and model and provides a new paradigm for complex random signal analysis.