Modular Decomposition of Learned Controlled Dynamics from One Fit

Learned models of controlled systems are often trained and deployed as monolithic predictors, even when the underlying physical system is organized into interacting subsystems that are built, operated, and maintained separately. Decomposing such a predictor usually requires choosing module boundaries and retraining a new model for each candidate structure. We study coupling-additive predictors, in which the prediction is a sum of contributions, one for each pair of a sensor group and a control channel; the class contains bilinear Koopman models with grouped dictionaries and any network with a linear head over per-group features. We introduce MODEC, which evaluates every candidate decomposition of a ridge-fitted predictor in this class from that single fit: the weights that restricted retraining would produce for any set of removed couplings, and the resulting increase in training loss, follow in closed form from the cached fit, and a covariance matrix of the fitted coupling contributions scores all candidate boundaries at once. On independent held-out episodes, a finite-sample bound on the cost of a restriction holds simultaneously over all candidate boundaries, with their number entering only through a logarithm. A selected decomposition runs as separate modules that reproduce the restricted predictor exactly, and a finite-horizon recursion bounds how its deviation from the original model accumulates over multi-step rollouts. On the Tennessee Eastman process and the IEEE 39-bus system, the scores rank the exact retraining cost of candidate modules with Spearman correlation 0.91 and 0.89, and the selected decompositions remove 67% and 84% of the removable couplings at 10% and 38% relative increases in one-step NRMSE; on a six-reactor cascade, MODEC recovers the planted subsystem structure at every coupling strength, with a restriction cost that becomes negligible when the subsystems are decoupled.