Machine Learning Surrogate Models for Mechanistic Kinetics: Embedding Atom Balance <i>and</i> 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 physical consistency 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 and a correction by linear interpolation backtracking which simultaneously guarantee both constraints. We demonstrate this using two practical examples from atmospheric chemistry and heterogeneous catalysis, as well as for a large number of random, synthetically generated reaction systems. In all cases, our approach yields exclusively positive model predictions conforming to the atom balance, without reducing the overall accuracy of the model.