Identifiability-aware neural ordinary differential equations for parsimonious and reliable dynamic modelling

Abstract

Neural ordinary differential equations (NODE) and hybrid NODE models provide flexible continuous-time representations of complex dynamic systems, but their expressive capacity can exceed the information content of the available data. Consequently, these models may reproduce observed trajectories while retaining weakly identifiable parameters, poorly constrained neural components, and unreliable extrapolation. Here we introduce identifiability-aware neural ordinary differential equations (iNODE), a framework that incorporates practical identifiability into neural differential equation design. iNODE models embed neural components as explicit analytic functions within the governing equations, enabling direct sensitivity analysis, Fisher-information-based confidence intervals, and identifiability-aware architecture selection. Candidate architectures are generated under data-support constraints, jointly calibrated, and ranked according to predictive accuracy, parsimony, and parameter identifiability. We evaluate the complete iNODE workflow against conventional NODE and hybrid NODE workflows representative of current practice using four controlled ground-truth benchmarks spanning fully data-driven and hybrid formulations, latent time-varying parameters, partial observability, and sparse or noisy measurements. Using the same training data and evaluation scenarios, the iNODE workflow selected more compact architectures, reduced parameter uncertainty, and improved extrapolation and recovery from latent-dynamics. These results establish practical identifiability as a model-design principle for parsimonious and reliable neural differential equations.