MENO: a hybrid matrix exponential-based neural operator for stiff dynamical systems

Abstract

Many systems in computational science are governed by stiff differential equations, where only a few variables contribute nonlinearly to the dynamics, while most affect it linearly. Traditional machine learning surrogates either ignore this structure or treat the entire system as a black box, limiting reliability and generalization. In this work, we present MENO (Matrix Exponential-based Neural Operator), a hybrid architecture that models the few nonlinear variables using conventional neural operators, while integrating the dominant linear time-varying subsystem, describing the dynamics of the remaining variables, through a novel neural matrix-exponential formulation. We apply MENO to three realistic thermochemical systems, demonstrating errors below 2% in zero-dimensional reactors and robust accuracy in multidimensional extrapolatory flows, alongside computational speedups of up to 4835× on GPU and 185× on CPU versus implicit solvers. We show that coupling machine learning with explicit mathematical and physical formulations yields rapid, accurate, and scalable simulations of stiff reactive dynamics.