Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows

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.

Data Assimilation with Deep Neural Nets Informed by Nudging

“…DNNs are known to learn ODEs/PDEs [5,16,25,30,40]. In case of stiff or chaotic systems [16], one idea is to learn one time step map, i.e., learn the update map u n−1 → u n .…”

“…DNNs are known to learn ODEs/PDEs [5,16,25,30,40]. In case of stiff or chaotic systems [16], one idea is to learn one time step map, i.e., learn the update map u n−1 → u n . The neural net takes as input the state at time t n−1 and the output is the approximate state at time t n .…”