Deep Residual Learning for Nonlinear Regression Deep learning plays a key role in the recent developments of machine learning. This paper develops a deep residual neural network (ResNet) for the regression of nonlinear functions. Convolutional layers and pooling layers are replaced by fully connected layers in the residual block. To evaluate the new regression model, we train and test neural networks with different depths and widths on simulated data, and we find the optimal parameters. We perform multiple numerical tests of the optimal regression model on multiple simulated data, and the results show that the new regression model behaves well on simulated data. Comparisons are also made between the optimal residual regression and other linear as well as nonlinear approximation techniques, such as lasso regression, decision tree, and support vector machine. The optimal residual regression model has better approximation capacity compared to the other models. Finally, the residual regression is applied into the prediction of a relative humidity series in the real world. Our study indicates that the residual regression model is stable and applicable in practice.

Rainfall Forecasting by using Residual Network with Cloud Image and Humidity This paper proposes a method of rainfall forecasting with high accuracy by combining two different types of information, cloud image data and humidity numerical data. The cloud image data is processed by using Residual network. By performing rainfall prediction using cloud images acquired from cameras instead of highly specialized weather data, it is easy to use the system for the end users. In addition to the cloud image data, this study introduces the humidity information that can be easily acquired to study, which brings more accurate rainfall forecasting. The combination of cloud images and humidity information realizes shorttime rainfall prediction with high accuracy of 95%.