Physics-Guided Neural Network with Model Discrepancy Based on Upper Troposphere Wind Prediction

In this paper, we focus on a method that integrates a physical model into a neural network. This study proposes a neural network that can predict two components, namely outputs based on a physical model and its model discrepancy. To achieve such a goal, we propose a novel neural network architecture and associated loss functions designed based on a target physical model. The physical model is used as a regularizer of spatial behavior where output from the neural network is used as an intermediate variable. Then, the model discrepancy is defined as its residual to the observation value. We also propose a network architecture which has Shared and Non-Shared networks, and the neural network can be trained by alternate optimization. We constructed the proposed method with wind prediction in the upper troposphere based on thermal wind equations as an example. The experimental results demonstrate that the proposed method can achieve higher predictive accuracy than normal convolutional neural network or using thermal wind equation, also the obtained model discrepancy expresses convergence and divergence of wind vectors.