A control‐inspired learning framework for stabilizing ill‐conditioned parameter recovery in hybrid models

First‐principles models provide mechanistic structure for chemical processes but may remain incomplete. Series‐type hybrid models compensate by embedding data‐driven components into first‐principles equations. However, training these components solely through output mismatch makes parameter recovery ill‐conditioned, as different missing physics can produce similar trajectories. To resolve this, we propose a control‐inspired hybrid model framework that adapts the input‐output feedback linearization theory by Daoutidis and Kravaris. By treating the missing physics as an unresolved parameter acting as an input‐like quantity, we construct a closed‐loop system to select a parameter proxy from measured data. This proxy ensures that the simulated model asymptotically tracks the measured output under minimum‐phase assumptions. The extracted proxy serves as the target for sparse dictionary‐based learning, ensuring the closure is learned from a tracking‐motivated signal rather than direct trajectory fitting. On a continuous stirred‐tank reactor, the learned sparse closure reproduces measured output while retaining the prescribed reaction‐rate channel.