From Features to States: Data-Driven Selection of Measured State Variables via RFE-DMDc

Abstract: The behavior of a dynamical system under a given set of inputs can be captured by tracking the response of an optimal subset of process variables (\textit{state variables}). For many engineering systems, however, first-principles, model-based identification is impractical, motivating data-driven approaches for Digital Twins used in control and diagnostics. In this paper, we present RFE-DMDc, a supervised, data-driven workflow that uses Recursive Feature Elimination (RFE) to select a minimal, physically meaningful set of variables to monitor and then derives a linear state-space model via Dynamic Mode Decomposition with Control (DMDc). The workflow includes a cross-subsystem selection step that mitigates feature \textit{overshadowing} in multi-component systems. To corroborate the results, we implement a GA-DMDc baseline that jointly optimizes the state set and model fit under a common accuracy cost on states and outputs. Across a truth-known RLC benchmark and a realistic Integrated Energy System (IES) with multiple thermally coupled components and thousands of candidate variables, RFE-DMDc consistently recovers compact state sets ((\approx 10) variables) that achieve test errors comparable to GA-DMDc while requiring an order of magnitude less computational time. The selected variables retain clear physical interpretation across subsystems, and the resulting models demonstrate competitive predictive accuracy, computational efficiency, and robustness to overfitting.