Guaranteed Mass-Conserving Deep Learning Model for Stiff Kinetics in Atmospheric Chemistry

Abstract

Atmospheric chemistry modeling faces significant computational challenges due to stiff coupled ordinary differential equation (ODE) systems with reaction rates spanning multiple orders of magnitude. Traditional numerical solvers have been computational bottlenecks in chemical transport models (CTMs), while existing deep learning approaches suffer from mass conservation violations and catastrophic error accumulation. To overcome the above issues, we propose mass-conserving flow matching (MC-Flow), a theoretically guaranteed mass-conserving deep learning model for stiff atmospheric chemistry ODEs. MC-Flow employs generative modeling that directly predicts final states from initial conditions, bypassing intermediate transitions to eliminate error accumulation. Moreover, we theoretically derive a guaranteed mass conservation constraint and modify the training and inference procedures within the flow matching framework according to the theorem. We validate the MC-Flow on H₂O₂/OH/HO₂ system, the Verwer system, and the tropospheric CH₄–CO–NO_x–HO_x chemical system. Results demonstrate significant improvement in accuracy, both for single-step and long-term predictions with 11-fold computational speedup over numerical solvers. MC-Flow maintains guaranteed mass conservation, while comparison methods show conservation violations. The study offers a physically consistent and computationally efficient alternative to conventional numerical methods, enabling potentially an AI-driven module for atmospheric chemistry modeling with applications in air quality and climate modeling.