Quantized Skeletal Learning (QSL): A Differentiable Programming Approach for Skeletal Reduction of Chemical Mechanisms

Abstract

This paper presents a data-driven approach, referred to as Quantized Skeletal Learning (QSL), for generating skeletal mechanisms. The approach has two key components: (1) a weight vector that can be used to eliminate relatively unimportant species and reactions, and (2) an end-to-end differentiable program whose loss-function gradients, with respect to the weight vector, can be used to adjust those weights. To promote sparsity in the weight vector -- and to reduce the influence of certain reactions or species to zero -- an $l_1$-regularized objective is employed alongside the standard mean squared error loss, thus removing the least important components. The proposed QSL approach is validated by generating skeletal mechanisms for methane and ethylene based on the GRI 3.0 and USC II mechanisms, respectively, demonstrating effectiveness in deriving skeletal mechanisms with various levels of fidelity. Two variants of QSL, designated as QSL-R and QSL-S, are tested; these focus on eliminating reactions and species, respectively. Analysis of ignition delay times and species mass fractions demonstrate QSL's capabilities to reliably and efficiently extract data-driven skeletal mechanisms of varying fidelities from detailed mechanisms.