Structure-Preserving Recurrent Neural Networks for a Class of Birkhoffian Systems

In this paper, the authors propose a neural network architecture designed specifically for a class of Birkhoffian systems — The Newtonian system. The proposed model utilizes recurrent neural networks (RNNs) and is based on a mathematical framework that ensures the preservation of the Birkhoffian structure. The authors demonstrate the effectiveness of the proposed model on a variety of problems for which preserving the Birkhoffian structure is important, including the linear damped oscillator, the Van der Pol equation, and a high-dimensional example. Compared with the unstructured baseline models, the Newtonian neural network (NNN) is more data efficient, and exhibits superior generalization ability.