Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability and poor convergence, which hinder effective rate coefficient estimation using learning-based approaches. To address this, we propose a Stiff Physics-Informed N eural ODE framework (SPIN-ODE) for chemical reaction modelling. Our method introduces a three-stage optimisation process: first, a black-box neural ODE is trained to fit concentration trajectories; second, a Chemical Reaction Neural Network (CRNN) is pre-trained to learn the mapping between concentrations and their time derivatives; and third, the rate coefficients are fine-tuned by integrating with the pre-trained CRNN. Extensive experiments on both synthetic and newly proposed real-world datasets validate the effectiveness and robustness of our approach. As the first work addressing stiff neural ODE for chemical rate coefficient discovery, our study opens promising directions for integrating neural networks with detailed chemistry.

It is well known that numerical simulations of high-speed reacting flows, in the framework of state-to-state formulations, are the most detailed but also often prohibitively computationally expensive. In this work, we start to investigate the possibilities offered by the use of machine learning methods for state-to-state approaches to alleviate such burden. In this regard, several tasks have been identified. Firstly, we assessed the potential of state-of-the-art data-driven regression models based on machine learning to predict the relaxation source terms which appear in the right-hand side of the state-to-state Euler system of equations for a one-dimensional reacting flow of a N$_2$/N binary mixture behind a plane shock wave. It is found that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, we investigated different strategies to speed-up our in-house state-to-state solver by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning methods into ordinary differential equations solvers may offer a speed-up of several orders of magnitude but some care should be paid for how and where such coupling is realized. Performances are found to be strongly dependent on the mutual nature of the interfaced codes. Finally, we aimed at inferring the full solution of the state-to-state Euler system of equations by means of a deep neural network completely by-passing the use of the state-to-state solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for these tasks.