Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows

TL;DR

This paper introduces novel deep neural network methods to efficiently approximate stiff ordinary differential equations in chemically reacting flows, significantly reducing computational costs and improving generalization.

Contribution

It proposes new DNN architectures tailored for stiff ODEs in reacting flows, comparing solution and derivative learning approaches, with demonstrated physical property integration.

Findings

DNNs effectively approximate stiff ODE solutions in reacting flows.

Incorporating physical properties improves DNN performance.

Proposed methods generalize well across different reactions.

Abstract

Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to the very large CPU requirements of chemical reactions (over 99%) a large number of flow and combustion problems are presently beyond the capabilities of even the largest supercomputers. Motivated by this, novel Deep Neural Networks (DNNs) are introduced to approximate stiff ODEs. Two approaches are compared, i.e., either learn the solution or the derivative of the solution to these ODEs. These DNNs are applied to multiple species and reactions common in chemically reacting flows. Experimental results show that it is helpful to account for the physical properties of species while designing DNNs. The proposed approach is shown to generalize well.