Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics

2026-06-01

AI Summary

This work addresses the challenge in polymerization reaction modeling where mechanistic models require cumbersome parameter calibration, while purely data-driven approaches suffer from limited experimental data availability during early design stages. To overcome this, the authors propose a Hybrid Neural Ordinary Differential Equation (Hybrid NODE) framework that preserves known physical principles—such as mass conservation—and employs a neural network solely to learn the unknown effective radical concentration term in the reaction kinetics. This approach achieves high predictive accuracy under extremely data-scarce conditions, yielding an RMSE of 0.013 with only ten non-uniformly sampled data points, even in the presence of noise and unseen operating conditions. The method significantly outperforms both a purely data-driven NODE (RMSE: 0.31) and discrete-time neural networks (RMSE: 0.68), effectively balancing physical consistency with data efficiency.

Abstract

Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.

Problem

• polymerization modeling
• incomplete kinetics
• data efficiency
• hybrid modeling
• Neural ODE

Innovation

• Hybrid Neural ODE
• data-efficient modeling
• polymerization kinetics
• mechanism-data fusion
• closure learning