Adjoint-based, in-situ optimization of neural network thermochemical manifolds

Current physics-based machine learning (ML) approaches to thermochemical manifold reduction have nearly universally been based on standard, offline optimization techniques. While successful for training, this does not guarantee a posteriori accuracy. We develop an ML technique to optimize neural network thermochemical models in-situ, that is, in conjunction with the partial differential equation (PDE) solver, by solving the adjoints of the forward PDEs. This ensures accuracy of the learned models when used for predictions. A two-part artificial neural network is used in which the first, linear portion maps from chemical species to a low-dimensional manifold and the second, nonlinear portion computes the manifold variable source terms and other quantities of interest. The model is pretrained offline followed by online adjoint-based optimization to improve a posteriori manifold and target variable trajectories. Testing is done on 1D shock-tube simulations of ethylene-air autoignition targeting ignition delay time, as indicated by a spike in the hydroxide mass fraction. This approach is intended to be used to generate accurate thermochemical manifolds for improved chemical kinetic predictions in large-eddy simulations.