Pattern formation in reaction-diffusion systems

The use of computational methods in modern science is growing rapidly. Many experiments are conducted in silico before they are conducted in the laboratory. The rapid advancement of computational resources and the development of novel algorithms has induced a paradigm shift in computational modeling. Whereas in the past modeling was typically conducted on a single time- and length-scale, contemporary modeling easily encompasses multiple such time- and length-scales.

In this research endeavor, a hierarchical reactor model is constructed wherein the fundamental kinetics are based on highly accurate microkinetic simulations. Although existing computational infrastructure can readily evaluate these microkinetic simulations simultaneously with reactor simulations, we here opt for a three-step procedure to investigate alternative algorithmic routes in the situation when the evaluation of the kinetic expressions proves to be computational infeasible.

The three-step procedure is as follows. First, a dataset consisting of many microkinetic simulations is constructed. Next, a neural network is trained using this dataset to calculate the intrinsic reaction rates based on external variables such as temperature and pressure. Finally, the neural network acts as the kinetic module in the overall reactor model. The major advantage of this computational strategy is that the evaluation of a neural network is significantly cheaper than the evaluation of the kinetic expressions. This holds true even in the case when the chemokinetic network consists of only a few elementary reaction steps.

Figure 1: Schematic depiction of an artifical neural network.

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