Lipschitz-Constrained Neural Networks for Robust Chemical Kinetics Modelling

The modeling of combustion chemistry kinetics is a computationally demanding task; the computational overhead increases exponentially in agreement with the number of chemical species considered. This computational cost is higher when considering multi-physical contexts, therefore, there is a need for time-efficient implementations. Nowadays, Machine Learning techniques promise reliable and accurate time-integration models at a lower computational cost, principally through the application of Neural Networks, however, they come with their drawbacks, such as the necessity of significant amounts of experimental data, and the costly training processes. Additionally, it is important to question the performance of the models when it comes to error amplification, principally when the model feeds itself iteratively. Indeed, many models present high accuracy when evaluated point by point in a time series, but cannot deal with the error propagation of small deviations that might occur when the initial condition is provided, developing wrong steady-states and outliers; therefore, the developed models should be robust enough to limit error propagation. In this work, an exploration of transitional states in the loss function is performed. The transitional states are expressed in terms of the Lipschitz constant; this consideration promises more robust performances in the form of Lipschitz-constrained neural networks. Such Lipschitz constant is defined as the maximum variable’s increase in a model without leading to divergence and will be implemented by adding a gradient term in the loss functions. Different network architectures will be tested, considering short and long networks, including a time-lag autoencoder architecture, due to its potential denoising properties. To keep the dimensionality manageable, Hydrogen combustion will be analyzed using the San Diego mechanism, without any loss of generalization.