| Artificial neural networks have primarily been utilized to solve problems in pattern recognition, decision-making, signal analysis and controls. This thesis investigates the use of networks in modeling physical systems in fluid mechanics by using the governing partial differential equations to initialize the network parameters. The initialization requires imposing certain constraints on the values of the input, bias, and output weights. The attribution of certain roles to each of these parameters allows for mapping a polynomial approximation into an artificial neural network architecture. This approach is shown to be capable of incorporating smooth neuron transfer functions, such as the popular hyperbolic tangent. Attention is focused on the two-dimensional Navier-Stokes equations for Boussinesq convection that model two-dimensional double diffusive convection. The network used to model this example utilizes an approximation of the Gudermannian function and an application of the pseudospectral method for complete network initiation. Numerical examples are presented illustrating the accuracy and utility of the method. |
