Bringing Chemistry to Scale: Loss Weight Adjustment for Multivariate
  Regression in Deep Learning of Thermochemical Processes
Franz M. Rohrhofer Stefan Posch Clemens Gößnitzer José M. García-Oliver Bernhard C. Geiger
Flamelet models are widely used in computational fluid dynamics to simulate
thermochemical processes in turbulent combustion. These models typically employ
memory-expensive lookup tables that are predetermined and represent the
combustion process to be simulated. Artificial neural networks (ANNs) offer a
deep learning approach that can store this tabular data using a small number of
network weights, potentially reducing the memory demands of complex simulations
by orders of magnitude. However, ANNs with standard training losses often
struggle with underrepresented targets in multivariate regression tasks, e.g.,
when learning minor species mass fractions as part of lookup tables. This paper
seeks to improve the accuracy of an ANN when learning multiple species mass
fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple,
yet effective loss weight adjustment that outperforms the standard mean-squared
error optimization and enables accurate learning of all species mass fractions,
even of minor species where the standard optimization completely fails.
Furthermore, we find that the loss weight adjustment leads to more balanced
gradients in the network training, which explains its effectiveness.