Fast uncertainty reduction of chemical kinetic models with complex spaces using hybrid response-surface networks

Abstract

Response-surface (RS) surrogate approaches permit efficient inverse uncertainty quantification (UQ) of combustion kinetic models, wherein the uncertainty of reaction rates is reduced from observed targets. For kinetic models with parameters characterized by large uncertainty factors, strong nonlinearities, and reaction couplings (e.g., reduced mechanisms of real fuels; such models are referred to be “complex” in this work), the global RS is difficult to approximate, precluding conventional surrogate approaches. This paper proposes a framework that is extendable to such systems, termed Hybrid Response Surface Networks followed by a Stochastic Gradient Descent Ensemble (HRSN-SGDE). This technique focuses on mapping the local RS of just the uncertain spaces in the vicinity of the observed target, referred to as the rate target subspace. Two neural network surrogates are considered: a classifier that predicts the probability of data residing in the rate target subspace and a local RS surrogate which maps the RS of this subspace. A hybrid surrogate loss function is then defined using these surrogates to optimize uncertain rates repeatedly to get an ensemble of solutions representing the constrained rate space. HRSN-SGDE is demonstrated on a complex jet fuel model developed using the hybrid chemistry (HyChem) approach with a low temperature chemistry sub-model using a series of ignition delay times as targets. Results show that the method's local RS objective enables efficient and accurate construction of the surrogates through active learning-based sampling. Also, the unique formulation of the surrogate loss function enables optimization that is robust to suboptimal local minima and faster than evolutionary algorithms by several orders of magnitude. It is shown that HRSN-SGDE method is highly efficacious and suitable to conducting inverse UQ on such complex kinetic models.