From PDEs to Wingbeats: A Novel Convolutional Fourier Layer-based ResNet Model

Béla János Szekeres, Natabara Máté Gyöngyössy, János Botzheim

Keywords: Fourier Neural Operator, ResNet, Insect wingbeat classification

Abstract: Recent advancements in Deep Learning apply Fourier Neural Operators (FNOs) for generating numerical solutions of Partial Differential Equations (PDEs). They are efficient due to their global spectral representations. However, their abilities in applied classification or regression tasks for time series have not been studied previously. We further investigate the motivation behind FNOs and provide a more detailed Discrete Fourier Transform-based definition. Furthermore, we introduce CF-ResNet-1D, a novel ResNet-inspired model built from Convolutional Fourier Layers being parallel units of FNO and 1D-Convolution. CF-ResNet-1D can perform time-series data analysis on raw time-domain signals while also taking advantage of the parallel spectral processing of the FNOs. This combined processing method outperforms spectrogram-based models for insect wingbeat sound classification, achieving state-of-the-art accuracy on benchmark datasets. The outcomes of our research offer promising insights about FNO application in real-world problems, such as mosquito management and the mitigation of insect-related diseases.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 5893