A liquid neural network with physical evolution for variable continuous time series prediction

Abstract

With the advantages of real-time computation and transparent decision-making process, Liquid time-constant neural networks (LTCs) perform well in modeling time-varying systems, but they also face problems such as the limitations of dependent learning capabilities and the adaptability to different data distributions. In order to improve the model learning performance, a liquid neural network with physical evolution for variable continuous time series prediction is proposed. Firstly, a simulation synaptic neural transmission model is combined with Hamilton evolution to establish a dynamic evolution model with physical states for neural information transfer. Then an explicit time-dependent Hamiltonian closed-form continuous-depth network (HCFC) is constructed to handle the transmission processing. The implicit Hamilton canonical equations are utilized to model the sophisticated nonlinear transformations experienced by the information as it propagates to the current neuron. The experimental results show that the HCFC model can improve the neural network dynamic property, enhance the learning performance, and provide superior performance in the prediction of complex continuous time series compared with the state-of-the-art (SOTA) methods.