Predictive Accuracy and Deep Ensemble Estimates of Epistemic Uncertainty in Constrained Neural ODEs for Kinetic Modeling

Abstract

Robust modeling of complex reaction systems requires not only accurate predictions and physical consistency, but also reliable estimation of predictive uncertainty. Here, we investigate how mechanistic constraint type influences the deep ensemble estimates of epistemic uncertainty in neural ordinary differential equations for catalytic kinetics. We impose atom-conservation constraints either softly through a learnable, time-dependent regularization strategy or exactly through a completion-based architecture that guarantees conservation by construction. The approaches are evaluated on real experimental data for stearic acid hydrodeoxygenation under data-scarce conditions, with the deep ensemble estimates of epistemic uncertainty quantified using deep ensembles. Constrained neural ordinary differential equations improve predictive accuracy relative to a mechanistic kinetic benchmark from 80% up to 93% for the best constrained model and reduce the deep ensemble estimates of epistemic uncertainty compared with its corresponding unconstrained model. Although the hard-constrained model produces narrower predictive distributions, these do not necessarily better reflect the observed data. These findings demonstrate that embedding conservation laws into neural ordinary differential equations improves predictive performance and uncertainty behavior, while highlighting the need to assess uncertainty calibration alongside uncertainty magnitude.