  Developing efficient and accurate algorithms for chemistry integration is a
challenging task due to its strong stiffness and high dimensionality. The
current work presents a deep learning-based numerical method called
DeepCombustion0.0 to solve stiff ordinary differential equation systems. The
homogeneous autoignition of DME/air mixture, including 54 species, is adopted
as an example to illustrate the validity and accuracy of the algorithm. The
training and testing datasets cover a wide range of temperature, pressure, and
mixture conditions between 750-1200 K, 30-50 atm, and equivalence ratio =
0.7-1.5. Both the first-stage low-temperature ignition (LTI) and the
second-stage high-temperature ignition (HTI) are considered. The methodology
highlights the importance of the adaptive data sampling techniques, power
transform preprocessing, and binary deep neural network (DNN) design. By using
the adaptive random samplings and appropriate power transforms, smooth
submanifolds in the state vector phase space are observed, on which two
three-layer DNNs can be appropriately trained. The neural networks are
end-to-end, which predict temporal gradients of the state vectors directly. The
results show that temporal evolutions predicted by DNN agree well with
traditional numerical methods in all state vector dimensions, including
temperature, pressure, and species concentrations. Besides, the ignition delay
time differences are within 1%. At the same time, the CPU time is reduced by
more than 20 times and 200 times compared with the HMTS and VODE method,
respectively. The current work demonstrates the enormous potential of applying
the deep learning algorithm in chemical kinetics and combustion modeling.
