Numerical characterization of distributed dynamic systems using tools of intelligent computing and generalized dimensional analysis

The hybrid use of generalized dimensional analysis – shortened to the acronym GDA – and neural networks is a powerful tool that can be employed for the solution of differential equations modeling physical processes. The GDA combines dimensional, inspectional, and also order of magnitude analysis in order to come up with the best scheme to reduce the number of variables in a problem. Its implementation reduces the input variable space, and thus reduces the number of training input vectors needed for model development. This leads to two positive effects: simulation time is reduced and more accuracy is achieved. The method is applied for the solution of sets of partial differential equations describing the performance of petroleum reservoirs. The results obtained prove the effectiveness of this approach when compared to the traditional discretisation simulation schemes.