Machine learning surrogate models for mechanistic kinetics: Embedding atom balance AND positivity

Multiscale simulations of reactive flows are critical in many fields. However, their application is often hindered by the high computational cost of solving detailed chemical kinetics. Recent advances in surrogate models for reactive chemistry offer promising speedups, but ensuring that these models remain physically consistent remains challenging. In particular, machine learning models for chemical kinetics must enforce atom balance and guarantee the positivity of predicted concentrations. Here, we introduce a positivity preserving projection that simultaneously enforces both constraints. We demonstrate this approach using an example from atmospheric chemistry and an example from heterogeneous catalysis. In both cases, the positivity preserving projection yields exclusively positive model predictions conforming to the atom balance, without reducing the overall accuracy of the model.