  Mathematical modeling is an essential step, for example, to analyze the
transient behavior of a dynamical process and to perform engineering studies
such as optimization and control. With the help of first-principles and expert
knowledge, a dynamic model can be built, but for complex dynamic processes,
appearing, e.g., in biology, chemical plants, neuroscience, financial markets,
this often remains an onerous task. Hence, data-driven modeling of the dynamics
process becomes an attractive choice and is supported by the rapid advancement
in sensor and measurement technology. A data-driven approach, namely operator
inference framework, models a dynamic process, where a particular structure of
the nonlinear term is assumed. In this work, we suggest combining the operator
inference with certain deep neural network approaches to infer the unknown
nonlinear dynamics of the system. The approach uses recent advancements in deep
learning and possible prior knowledge of the process if possible. We also
briefly discuss several extensions and advantages of the proposed methodology.
We demonstrate that the proposed methodology accomplishes the desired tasks for
dynamics processes encountered in neural dynamics and the glycolytic
oscillator.
