An embedded Hamiltonian dynamic evolutionary neural network model for high-dimensional data recognition

Abstract

Aiming at the limitation of Hamiltonian neural network in high-dimensional data processing with non-observable physical quantity system, an embedded Hamiltonian dynamic evolutionary neural network model (EHDN) is proposed in this paper. First, the dynamic physical quantities of high dimensional nonlinear systems are represented by constructing Hamiltonian functions. Then a symplectic integrator is designed to realize the time-varying evolution of network features based on Hamiltonian regular equation and variational numerical integration. Finally, the Hamiltonian dynamic evolutionary neural network is embedded in the convolutional neural network (CNN) to realize the Hamiltonian simulation evolution of convolutional features. Experimental results on two different datasets, CIFAR and Fashion-Mnist, show that compared with existing state-of-the-art (SOTA) methods, EHDN model can combine the advantages of Hamiltonian dynamics and convolutional network to improve the recognition accuracy and training stability in high-dimensional image classification tasks.