Transfer learning for predicting source terms of principal component transport in chemically reactive flow

TL;DR

This work tackles data-sparsity in data-driven reduced-order models for chemically reactive flows by combining a PCA-based ROM (PC-transport ROM) with ANNs to tabulate PC reaction rates and predict ignition dynamics in a 0-D hydrogen/air system. It systematically evaluates transfer-learning strategies (TL1, TL2, TL3) and introduces PaPIR, a unified framework that jointly tunes initialization via $\lambda_2$ and regularization via $\lambda_1$ to maximize predictive accuracy under sparse data. The key finding is that TL3 with an optimal $\lambda_1$ can dramatically reduce the required target data (up to ~8×) and improve $\tau_{\rm ig}$ predictions, while PaPIR delivers additional gains, especially when source-target task similarity is low, enabling robust extrapolation across $\phi$ and higher $T_0$. These results advance data-efficient surrogate modeling for ignition and kinetic problems, potentially reducing the need for expensive high-fidelity data in reactive-flow simulations.

Abstract

The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven reduced-order model that represents the homogeneous ignition process of a hydrogen/air mixture. Principal component analysis is applied to reduce the dimensionality of the hydrogen/air mixture in composition space. Artificial neural networks (ANNs) are used to tabulate the reaction rates of principal components, and subsequently, a system of ordinary differential equations is solved. As the number of training samples decreases at the target task (i.e.,for T0 > 1000 K and various phi), the reduced-order model fails to predict the ignition evolution of a hydrogen/air mixture. Three transfer learning strategies are then applied to the training of the ANN model with a sparse dataset. The performance of the reduced-order model with a sparse dataset is found to be remarkably enhanced if the training of the ANN model is restricted by a regularization term that controls the degree of knowledge transfer from source to target tasks. To this end, a novel transfer learning method is introduced, parameter control via partial initialization and regularization (PaPIR), whereby the amount of knowledge transferred is systemically adjusted for the initialization and regularization of the ANN model in the target task. It is found that an additional performance gain can be achieved by changing the initialization scheme of the ANN model in the target task when the task similarity between source and target tasks is relatively low.

Figures (14)

• Figure 1: Variations in 0-D ignition delay time, $\tau_{\rm{ig}}$, of the hydrogen/air mixture for different initial temperature, $T_0$, as a function of equivalence ratio, $\phi$. In the present study, it is assumed that the number of training samples at the source task ($T_0$ = 1000 K) is sufficient, while the number of training samples at the target tasks ($T_0 >$ 1000 K) is sparse.
• Figure 2: Modes of the first five PCs depending on the training dataset varying $T_0$ with $N_{\phi}$ of 30.
• Figure 3: Temporal evolution of the first three principal components for three different equivalence ratios, $\phi$, of 0.85, 1.35, and 2.95, obtained by projecting $\textbf{A}^{\rm{T}}$ onto the FOM result. The vertical lines in (a) represent the ignition delay time for different $\phi$. Here, the ignition delay time is defined by the time at which the temperature gradient reaches its maximum value.
• Figure 4: Variations in (a) 0-D ignition delay time, $\tau_{\rm{ig}}$, predicted by FOM (solid symbol) and PC-transport ROM (dashed-dot line), and (b) the relative-error of the PC-transport ROM compared with FOM for the homogeneous hydrogen/air mixture with various $\phi$ (i.e., $\phi$ = 0.15 $\sim$ 2.95; $\Delta \phi$ =0.1) at $T_0$ = 1000 K.
• Figure 5: Temporal evolution of the thermochemical state scalars of a homogeneous hydrogen/air mixture at $T_0$ = 1000 K and $\phi$ = 1.35. Solid line: FOM result, Dashed line: reconstructed from the PC-transport ROM result with $N_{\phi}$ = 30.