A data-driven reduced-order model for stiff chemical kinetics using dynamics-informed training

A data-based reduced-order model (ROM) is developed to accelerate the time integration of stiff chemically reacting systems by effectively removing the stiffness arising from a wide spectrum of chemical time scales. Specifically, the objective of this work is to develop a ROM that acts as a non-stiff surrogate model for the time evolution of the thermochemical state vector (temperature and species mass fractions) during an otherwise highly stiff and nonlinear ignition process. The model follows an encode-forecast-decode strategy that combines a nonlinear autoencoder (AE) for dimensionality reduction (encode and decode steps) with a neural ordinary differential equation (NODE) for modeling the dynamical system in the AE-provided latent space (forecasting step). By means of detailed timescale analysis by leveraging the dynamical system Jacobians, this work shows how data-based projection operators provided by autoencoders can inherently construct the latent spaces by removing unnecessary fast timescales, even more effectively than physics-based counterparts based on an eigenvalue analysis. A key finding is that the most significant degree of stiffness reduction is achieved through an end-to-end training strategy, where both AE and neural ODE parameters are optimized simultaneously, allowing the discovered latent space to be dynamics-informed. In addition to end-to-end training, this work highlights the vital contribution of AE nonlinearity in the stiffness reduction task. For the prediction of homogeneous ignition phenomena for H2-air and C2H4-air mixtures, the proposed ROM achieves several orders-of-magnitude increase in the integration time step size when compared to (a) a baseline CVODE solver for the full-chemical system, (b) statistical technique – principal component analysis (PCA), and (c) computational singular perturbation (CSP), a vetted physics-based stiffness-reducing modeling framework.