Optimization and Computational Fluid Dynamics - Department of ...

162 René A. Van den Braembussche
Fig. 6.10 Architecture of a three-layer ANN
6.3.1 Artificial Neural Networks
Artificial Neural Networks (ANN) are used to predict the performance of a
new geometry by means of the information contained in the database. This
requires the learning of the relation between the n input data (geometry
parameters) of a process (NS solver) and the m outputs of the process (mass
flow, efficiency, local pressures and temperatures, velocities, etc.). The use
of an exact ANN predictor could reduce the effort to one design cycle by
the GA. Hence, improving the accuracy of the ANN will shorten the design
process.
An ANN (Fig. 6.10) is composed of n,k,m elementary processing units
called neurons or nodes. These nodes are organized in layers and joined with
connections (synapses) of different intensity, called the connection weight (W)
to form a parallel architecture. Each node performs two operations: the first
one is the summation of all the incoming signals and a bias bi, the second
one is the transformation of the signal by using a transfer function (FT). For
the first layer this corresponds to:
⎛
⎞
n�
a1(i)=FT1 ⎝ W1(i,j).n(j)+b1(i) ⎠
j=1
A network is generally composed of several layers: an input layer, zero,
one or more hidden layers and one output layer. The coefficients are defined
by a learning procedure relating the output to the input data.
The main purpose of ANN is not to reproduce the existing database with
maximum accuracy but to predict the performance of new geometries it has
not seen before, i.e., to generalize. A well-trained ANN may show a less