ReCurveflow: A Flow Matching Framework that Learns Curved Reaction Trajectories to Predict Transition State Geometries

Transition-state (TS) structures define the energetic barriers and mechanistic pathways of elementary chemical reactions, yet their identification remains computationally demanding because conventional saddle-point searches require expensive quantum-mechanical calculations. Recent machine-learning approaches have accelerated TS generation by predicting structures from reaction endpoint information, but they primarily learn geometric correspondence between endpoints and TSs, leaving the structural transformations underlying elementary reactions implicitly represented. To address this limitation, we introduce TransTS, a reaction-transformation-aware framework for generalizable TS generation from atom-mapped reactant-product pairs. TransTS explicitly learns atom-level structural transformations between reaction endpoints and integrates them with a unified atom-aligned geometric representation of reactants, TSs and products, enabling reaction-aware equivariant generation of TS geometries. TransTS is designed to provide reliable TS initial guesses for subsequent quantum-chemical refinement, where generated structures are evaluated not only by geometric similarity but also by their ability to converge to validated saddle points and recover the intended reaction pathways. Across IID and zero-shot OOD benchmarks, TransTS demonstrates improved TS initialization quality, with particularly strong generalization to unseen reaction distributions. On the challenging GDB-10-rxn and GDB-17-rxn OOD benchmarks, TransTS generates TS candidates that more frequently converge to validated saddle points and recover the intended elementary reactions after refinement than existing approaches under the same training regime. Scaling reaction coverage and model capacity further improves both geometric fidelity and refinement outcomes.

Chemical reactions are fundamentally transformations in electron space, yet most machine learning approaches model them either through de novo generation of product molecules or through heuristic graph edits that operate directly on molecular topology. We introduce MAELLE (MechAnistic Edit fLow-matching on eLectron rEarrangements), which instead models reactions as discrete flow matching over electron occupation vectors. Concretely, we formulate the reactant-to-product mapping as a Continuous-time Markov Chain (CTMC) over the graph-structured integer-valued electron occupation space defined on all bonding, non-bonding, and hydrogen sites. To construct the interpolants between the reactants and products, we generalize the discrete flow matching mixture path to an edit-based formulation, where the electron moves are interpolated using Optimal Transport, yielding a mechanism-like set of moves without elementary step annotations. MAELLE achieves competitive performance on the USPTO-480K benchmark compared with leading reaction prediction models. Beyond in-distribution learning, we evaluate robustness across two out-of-distribution settings - structural complexity and reaction type - and find that MAELLE maintains strong performance where existing methods degrade. Finally, because the learned flow operates over the full electron redistribution, MAELLE naturally recovers mechanistic trajectories that align with known chemistry and can predict side products of a reaction.

Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate. Both minimize quadratic functionals over the reactive path ensemble, analogous to the flow matching loss in generative modeling, and require no knowledge of the underlying dynamics or stationary distribution. Unlike committor-based methods, $u$ and $h$ remain well-defined under projection onto non-Markovian collective variables, and their level sets in turn provide adaptive interfaces for improved sampling with enhanced sampling methods. Flux Matching is validated through the generation of current velocity trajectories and rate constant calculations on molecular systems.