Modelling of 1-D pure advection processes using artificial neural networks

Using the results of some simple numerical experiments, it has been shown that, in the simplest case of one-dimensional pure advection with a constant velocity, a linear artificial neural network (ANN) is capable of learning the exact solution, which is also exactly equivalent to the differential equation description. In this way, the ANN is being used as numerical operator that contains the same knowledge, or has the same semantic content, as the governing partial differential equations.