Hybridised mechanistic and machine learning digital twins for modelling and optimising chemical processes in flow: A comparative analysis of parallel and series-based hybridisation

In the field of chemical engineering, accurate prediction of reaction kinetics and concentration profiles is critical for the design and optimisation of industrial processes. However, achieving accurate predictions under variable or limited data conditions remains a major challenge. Despite the growing interest in hybrid models, a systematic comparison of parallel and series-based hybridisation strategies using empirical flow reactor data for digital twin applications has not yet been established. Here we show that PINN architecture can accurately predict concentration profiles and estimate reaction rate constants under both data-rich and data-scarce conditions, while the SPH+GA framework enhances spatial simulation fidelity and enables system-level optimisation through particle-based modelling. The same PINN architecture can be effectively applied in both forward and inverse modes, accurately predicting concentration profiles and estimating reaction rate constants with errors under 2%, even in data-scarce conditions. The SPH+GA framework enables detailed particle-level simulation and global optimisation, offering insight into spatial dynamics and reactor mixing. This series hybrid model achieved an R${}^2$ up to 0.91 and enabled flexible system tuning. These results underscore the broader value of hybrid mechanistic–machine learning frameworks, particularly for process environments with limited or noisy data. Our findings highlight that while PINNs offer high predictive accuracy and lower computational cost, SPH+GA excels in resolving spatial dynamics and supporting system characterisation. These parallel and series hybrid strategies demonstrate complementary strengths for building robust digital twins of chemical processes.