Neural-network placement in physics-informed machine learning for mechanistic process-model repair: a case study in industrial coffee roasting

Abstract Mechanistic process models are central to industrial simulation and control, but their rollout accuracy often depends on run-specific initialization data that archival production telemetry cannot reliably provide. This gap can leave predictions inaccurate even when the underlying physical scaffold is approximately correct. Physics-informed machine learning (PIML) can be used to repair such models from data, yet many comparisons do not isolate a key design choice: where the learned neural network is placed relative to the mechanistic ordinary differential equation (ODE). Using a 221-roast industrial coffee-roasting cohort, this study compares four PIML repair strategies and a matched-input neural baseline as a six-model placement spectrum, holding the learned network family fixed (feedforward multilayer perceptron, MLP) so that the primary design variable is neural-network placement rather than neural architecture. The four PIML strategies lift autonomous-rollout $$\\hbox {R}^{2}$$ from -0.44 to 0.70-0.94; the matched-input neural baseline reaches 0.97 with 3-20 times fewer parameters than every PIML strategy tested. Three structural findings characterize the spectrum. First, the PIML strategies tend to share their hard roasts (per-roast Pearson r approximately 0.5-0.9), whereas the neural baseline identifies a different set of hard roasts (r approximately 0), reaching a comparable predictive ceiling through structurally different failure profiles. Second, in this benchmark a physics-motivated bound on the residual correction costs more than it buys: the unbounded variant uses 3.7 times fewer parameters while improving $$\\hbox {R}^{2}$$ by 0.02. Third, seed stability varies by more than an order of magnitude across PIML strategies (range 0.009 to 0.117 $$\\hbox {R}^{2}$$ across five or more retraining seeds). These findings suggest that, for this metadata-limited cohort, physics-informed scaffolds are effective repair mechanisms for mechanistic rollouts, but they do not automatically provide better parameter efficiency or optimization stability than a compact matched-input empirical baseline.