A New Robust Learning Algorithm for Ordinary Differential Equation Network

The data modeling of complex systems typically exhibits characteristics such as strong nonlinearity, variable redundancy, and abnormal data, all of which tend to decrease the model performance. To solve these problems, a robust learning algorithm for an ordinary differential equation (ODE) network is proposed. Firstly, the ODE network is trained as the basic model. Secondly, a novel loss function combines a Huber loss with elastic net regularization technique is designed. The proposed loss function has excellent resistance to outliers in the data and can make the model genialize better. Thirdly, a nonnegative garrote algorithm is introduced to reduce the redundancy of input variables and the model complexity. Finally, the effectiveness of the proposed algorithm is verified on a time series Friedman dataset and an industrial process dataset, compared with other data-driven modeling algorithms. Simulation results demonstrate that the proposed algorithm can effectively select relevant input variables, simplify the model structure, and improve the generalization performance of the model.