2.3.2. Temporal Convolutional Network for Daily Population Loss Rate Forecasting

A temporal convolutional network (TCN) [20] was used to forecast the future honey bee daily population loss rate and predict potential colony collapse. The key characteristic of TCNs is its usage of convolutions. Convolutions are causal and does not depend on any future timestep data. Unlike other deep learning models for forecasting like GRU and LSTM. TCN has longer memory and can process time series data of any length and generate similar long predictions [25]. For these reasons, TCN was selected as the forecasting model in this work.

The TCN forecasting model comprised a series of blocks, which individually contained a sequence of convolutional layers. Each layer was composed of dilated convolutions, associated with a dilation factor d, with rectified linear unit (ReLU) as non-linear activation function. Dilation introduces a fixed step between every adjacent filter. Larger dilations and larger filters of size k effectively expand the receptive field [19,20]. In these convolutions, exponential increments in the value of d increases the depth of the network. This guarantees the presence of a filter that hits each input within the effective history [19]. A residual connection was added for each dilated convolution to integrate the convolutional result with the input layer. In this work, the input of the TCN model was defined as xt and the output was represented by yt, where xt contains n-dimensional parameters. The output of the TCN model was the LR of the next day.

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