Quadratic Residual Multiplicative Filter Neural Networks for Efficient Approximation of Complex Sensor Signals

In this research, we present an innovative Quadratic Residual Multiplicative Filter Neural Network (QRMFNN) to effectively learn extremely complex sensor signals as a low-dimensional regression problem. Based on this novel neural network model, we introduce two enhanced architectures, namely FourierQResNet and GaborQResNet. These networks integrate the benefits of quadratic residual neural networks, multiplicative filter neural networks, and several filters in signal processing to effectively capture complex signal patterns, thereby addressing issues associated with convergence speed, precision, and spectral bias. These architectures indicate effectiveness in reducing spectral bias, thereby improving the accuracy of signal approximation. After conducting comprehensive experiments on ten very complex test signals from diverse application domains, the proposed architectures have demonstrated superior ability in approximating intricate sensor signals and mitigating spectral bias effectively. The numerical results of the experiments reveal that FourierQResNet and GaborQResNet exhibit excellent performance compared to other existing neural network architectures and models in accurately estimating complicated sensor signals, with admiringly small errors. In addition, the findings emphasize the importance of mitigating spectral bias in order to achieve reliable learning from sensor data. The implications of these results are significant in various domains that require precise and reliable sensor data analysis, including healthcare, environmental monitoring, aviation, IoT applications, and industrial automation. This research significantly advances the field of sensor signal approximation and opens new avenues for enhancing data interpretation reliability and accuracy in complex signal environments.