Deep learning of nonlinear development of unstable flame fronts

Abstract: The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. From the generated solution functions an operator is trained to map the function to a future solution function after a small time-step. The goal is for this operator to be able to accurately map long sequences of solutions through repeated application of the operator. Two networks were trained for this task, a Convolutional Neural Network and A Fourier Neural Operator. The investigation found that the operator were not only able to accurately predict fairly long sequences, but was also able to capture the long-term characteristics of the flame front development. This study also shows that it is possible with specific modifications to a Convolutional Neural Network proposed in the study, a single Neural Network is able to make accurate recurrent predictions for multiple values of a parameter affecting the solution of the partial differential equation considered.