Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Artificial neural network model
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  max_nodes  Maximum number of hidden layer nodes  
Optional  range  Range for neural network random weights  
Optional  random_weight  (Inactive) Random weight control  
Optional  export_model  Exports surrogate model in userselected format 
Dakota's artificial neural network surrogate is a stochastic layered perceptron network, with a single hidden layer. Weights for the input layer are chosen randomly, while those in the hidden layer are estimated from data using a variant of the Zimmerman direct training approach[92].
This typically yields lower training cost than traditional neural networks, yet good outofsample performance. This is helpful in surrogatebased optimization and optimization under uncertainty, where multiple surrogates may be repeatedly constructed during the optimization process, e.g., a surrogate per response function, and a new surrogate for each optimization iteration.
The neural network is a non parametric surface fitting method. Thus, along with Kriging (Gaussian Process) and MARS, it can be used to model data trends that have slope discontinuities as well as multiple maxima and minima. However, unlike Kriging, the neural network surrogate is not guaranteed to interpolate the data from which it was constructed.
This surrogate can be constructed from fewer than data points, however, it is a good rule of thumb to use at least data points when possible.
The form of the neural network model is
where is the evaluation point in dimensional parameter space; the terms are the random input layer weight matrix and bias vector, respectively; and are a weight vector and bias scalar, respectively, estimated from training data. These coefficients are analogous to the polynomial coefficients obtained from regression to training data. The neural network uses a cross validationbased orthogonal matching pursuit solver to determine the optimal number of nodes and to solve for the weights and offsets.