Data-integrated low-dimensional surrogate models with guarantees

This project addresses obtaining a low-dimensional realization of a stable and passive dynamical system from given data samples. We will use the energy-based modeling framework of port-Hamiltonian systems – an extension of Hamiltonian systems to open physical systems – to construct a surrogate model solely from (measurement) data reflecting the physical properties of the original system. The data used to build the surrogate model may be available either in the time or frequency domain. A pivotal question underlying this investigation is to guarantee the physical behavior of coupled dynamical systems learned from data and (partial) differential-algebraic equations derived from first-principles. To achieve this goal, we reformulate infinite-dimensional problems that are important in developing a digital human model as port-Hamiltonian systems. We develop novel structure-preserving model-order reduction strategies to facilitate a fast evaluation of the models and complement the system identification methods.