Quantification of Exogenous Drivers’ Impact on System Dynamics

A dynamic system may vary with time via dependencies of its underlying parameters on exogenous variables. Learning about if/how variation of an exogenous variable affects the dynamic system based on observational data is important for analysis, prediction, and control of the dynamic system. This work proposes a method to quantify the impact of exogenous drivers of a dynamic system given observations from the system’s state variables. This is accomplished by performing a modal decomposition of the dynamic operator and quantifying modal similarities. Numerical experiments demonstrate successful application of the proposed method to identify causal drivers of systems governed by common differential equations, i.e, diffusion process and oscillatory models. The proposed method enables investigating the dependence of decay rate, oscillation frequency, and spatial modes of the dynamic system on the exogenous drivers.