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

TL;DR

This work addresses the challenge of reducing chemical mechanisms for combustion simulations by learning sparse, data-driven skeletal representations through differentiable programming. The authors introduce Quantized Skeletal Learning (QSL), which jointly learns a weighting vector over reactions or species and backpropagates through the ODE solver to minimize trajectory mismatch with an $L_1$-regularized loss, implemented in JAX. They instantiate two variants, QSL-R (reaction elimination) and QSL-S (species elimination), and validate on methane (GRI Mech 3.0) and ethylene (USC Mech II), achieving compact skeletons with varying fidelity and improved ignition-delay predictions compared to DRGEP. The method records a notable computational cost, but offers a data-driven route to structurally meaningful reductions, with future work aiming at scaling to larger mechanisms and leveraging accelerators.

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.

Figures (11)

• Figure 1: Illustration of QSL approach, involving a forward pass where weighted source terms are employed to advance the solution in time, followed by a backpropagation through all the operations of the solver and chemical kinetics model to modify the weighting vector, $\bm \alpha$.
• Figure 2: Sigmoid activation used to constrain weights to the interval [0, 1].
• Figure 3: Number of reactions as a function of the level of regulariation.
• Figure 4: Ignition delay as a function of 1000/T for various levels of equivalence ratio and pressure for $\kappa = 10^{-4}$.
• Figure 5: Steady-state concentrations of thermochemical scalars.