Physics-informed machine learning for modeling multidimensional dynamics

This study presents a hybrid modeling approach that integrates physics and machine learning for modeling multi-dimensional dynamics of a coupled nonlinear dynamical system. This approach leverages principles from classical mechanics, such as the Euler-Lagrange and Hamiltonian formalisms, to facilitate the process of learning from data. The hybrid model incorporates single or multiple artificial neural networks within a customized computational graph designed based on the physics of the problem. The customization minimizes the potential of violating the underlying physics and maximizes the efficiency of information flow within the model. The capabilities of this approach are investigated for various multidimensional modeling scenarios using different configurations of a coupled nonlinear dynamical system. It is demonstrated that, in addition to improving modeling criteria such as accuracy and consistency with physics, this approach provides additional modeling benefits. The hybrid model implements a physics-based architecture, enabling the direct alteration of both conservative and non-conservative components of the dynamics. This allows for an expansion in the model’s input dimensionality and optimal allocation of input variable effects on conservative or non-conservative components of dynamics.