This section describes the DeepONet architecture 27 (see Figs. and) used to construct the surrogate components for the energy-transfer reaction rates by extracting characteristic patterns from the data. As already discussed, Fig. shows a contour plot of the inelastic rate coefficients for a fixed value of the translational temperature. The maximum in the contour identifies the initial state (as the elastic rate coefficient corresponds to the highest value), and the different colors correspond to the likelihood of transitions. The rate coefficients that characterize processes starting from a given state take the form of ellipsoidal kernels Preprint centered at the initial reactant state. The main objective is to learn these transition kernels and represent them through a DeepONet. The DeepONet architecture consists of two sub-networks, referred to as the branch and the trunk, which are connected by a dot-product layer. This composite structure allows the representation of the output quantity as a linear combination, in which modes and components are constructed in two independent input spaces by the trunk and branch, respectively. By identifying the trunk outputs as t k and the branch outputs as b k , the inelastic/exchange rate coefficient is computed as: