DoE-SINDy: an automated framework for model generation and selection in kinetic studies

Efficient and accurate identification of kinetic models is critical for understanding chemical reaction mechanisms and enabling process optimization and control. This study introduces DoE-SINDy, an enhanced framework that integrates design of experiments (DoE) with the Sparse Identification of Nonlinear Dynamics (SINDy) methodology to improve the reliability and interpretability of identified models under constraints of noisy, sparse and small-size experimental data sets. Unlike existing approaches, DoE-SINDy employs iterative subset sampling for model generation, reducing the inclusion of biased trajectories and ensuring the identification of a representative model structure. The framework further incorporates parameter re-estimation, non-significant terms removal, and identifiability analysis to enhance model robustness, reduce complexity, and reject overly complex or non-identifiable models. Rigorous model evaluation and selection steps, guided by flexible stopping criteria, strike a balance between statistical accuracy and computational efficiency. The methodology is evaluated through a simulated case study on a batch reaction system, where DoE-SINDy consistently outperforms original SINDy and ensemble-SINDy (ESINDy) in recovering ground-truth models and achieving convergence to optimal structures as the experimental dataset grows.