Transfer learning of data-driven crystallisation processes via constrained Neural Ordinary Differential Equations

Abstract

Modelling complex crystallisation processes remains challenging due to limited experimental datasets, high measurement noise, and the need for generalisability across varying operating conditions. Neural Ordinary Differential Equations (NODEs) and transfer learning (TL) offer promising tools to overcome these limitations by providing data-efficient, flexible, and transferable modelling frameworks. This work investigates the use of NODEs to model protein crystallisation dynamics under data-scarce conditions. A NODE trained on a data-rich source system successfully captures solute consumption and particle size dynamics, but when applied to data-sparse target systems, scratch-trained NODEs exhibit limited generalisation and unphysical behaviours. To address this, several TL strategies are evaluated, including layer freezing, parameter deviation penalisation, and system-embedding within the neural architecture. Results show that layer freezing and deviation penalty consistently improve knowledge transfer, while system-embedding offers robustness in noisy or undersampled datasets. In addition, physics-informed NODEs, constrained to enforce monotonic concentration decay and crystal growth, demonstrate greater stability under high noise and sparse measurement regimes, ensuring physically consistent predictions. Overall, the combination of constrained NODEs with appropriate TL strategies provides a robust framework for accurate, transferable modelling of crystallisation systems in low-data regimes.