Hybrid Modeling of a Multidimensional Coupled Nonlinear System With Integration of Hamiltonian Mechanics

Abstract

This study concerns hybrid modeling of a multidimensional coupled nonlinear system. The underlying basis for the model is derived from Hamiltonian mechanics capitalizing on the broad utility and efficiency of energy-based reasoning in modeling high-dimensional systems. The hybrid model is essentially an artificial neural network with a computational graph that is modified from conventional neural networks in a few significant ways. The first modification includes incorporating an intermediate scalar function representing the Hamiltonian learned from data. The second modification enhances input/output channels for capturing the multidimensional dynamics of the system. The main goal of such hybrid reasoning is to improve the extrapolation capability of the model by enforcing conformance with some key aspects of the underlying physics in the form of a bias. The results demonstrate that incorporating this physics-based bias into the hybrid model empowers it to produce long-term and physically plausible predictions. The proposed modeling approach also shows high scalability for energy-based modeling of multidimensional dynamic systems in general.