A novel loss function of deep learning in wind speed forecasting

Wind speed forecasting is an essential task in improving the efficiency of the energy supply. Currently, deep learning models have become extremely popular, where the traditional mean squared error (MSE) loss function is often employed. Unfortunately, the MSE loss function cannot accurately measure the nonlinearity of wind speed data, and new loss functions have seldom been developed for wind speed forecasting. In addition, the MSE loss function is sensitive to outliers, degrading the stability. To address these problems, we propose a kernel MSE loss function to evaluate the ubiquitous nonlinearity of deep learning errors in the reproducing kernel Hilbert space. The new loss function utilizes the kernel skills in the loss function of deep learning methods for the first time. The first and second derivatives of the new loss function guarantee the robustness against outliers. The experimental results with three fundamental deep learning methods on three public datasets validate that the new loss function is efficient and superior in most cases, and its resultant error can be 95% smaller than MSE in multiple step prediction. The results imply that developing a loss function with kernel skills is a new way to get better results.