Hong G. Im

Mert Yakup Baykan, Weitao Liu, Thorsten Zirwes et al.

A novel convolutional autoencoder neural ODE (CAE-NODE) framework is proposed for a reduced-order model (ROM) of transient 2D counterflow flames, as an extension of AE-NODE methods in homogeneous reactive systems to spatially resolved flows. The spatial correlations of the multidimensional fields are extracted by the convolutional layers, allowing CAE to autonomously construct a physically consistent 6D continuous latent manifold by compressing high-fidelity 2D snapshots (256x256 grid, 21 variables) by over 100,000 times. The NODE is subsequently trained to describe the continuous-time dynamics on the non-linear manifold, enabling the prediction of the full temporal evolution of the flames by integrating forward in time from an initial condition. The results demonstrate that the network can accurately capture the entire transient process, including ignition, flame propagation, and the gradual transition to a non-premixed condition, with relative errors less than ~2% for major species. This study, for the first time, highlights the potential of CAE-NODE for surrogate modeling of unsteady dynamics of multi-dimensional reacting flows.

Vijayamanikandan Vijayarangan, Harshavardhana A. Uranakara, Francisco E. Hernández-Pérez et al.

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our recent study [1] reported that an autoencoder (AE) combined with neural ODE (NODE) as a surrogate reduced order model (ROM) for the integration of stiff chemically reacting systems led to a significant reduction in the temporal stiffness, and the behavior was attributed to the identification of a slow invariant manifold by the nonlinear projection of the AE. The present work offers fundamental understanding of the mechanism by employing concepts from information theory and better mixing. The learning mechanism of both the encoder and decoder are explained by plotting the evolution of mutual information and identifying two different phases. Subsequently, the density distribution is plotted for the physical and latent variables, which shows the transformation of the \emph{rare event} in the physical space to a \emph{highly likely} (more probable) event in the latent space provided by the nonlinear autoencoder. Finally, the nonlinear transformation leading to density redistribution is explained using concepts from information theory and probability.