Hr. Maier et Gc. Dandy, Empirical comparison of various methods for training feed-forward neural networks for salinity forecasting, WATER RES R, 35(8), 1999, pp. 2591-2596
Feed-forward artificial neural networks (ANNs) are being used increasingly
to model water resources variables. In this technical note, six methods for
optimizing the connection weights of feedforward ANNs are investigated in
terms of generalization ability, parsimony, and training speed. These inclu
de the generalized delta (GD) rule, the normalized cumulative delta (NCD) r
ule, the delta-bar-delta (DBD) algorithm, the extended-delta-bar-delta (EDB
D) algorithm, the QuickProp (QP) algorithm, and the MaxProp (MP) algorithm.
Each of these algorithms is applied to a particular case study, the foreca
sting of salinity in the River Murray at Murray Bridge, South Australia. Th
irty models are developed for each algorithm, starting from different posit
ions in weight space. The results obtained indicate that the generalization
ability of the first-order methods investigated (i.e., GD, NCD, DBD, and E
DBD) is better than that of the second-order algorithms (i.e., QP and MP).
When the prediction errors are averaged over the 30 trials carried out, the
performance of the first-order methods in which the size of the steps take
n in weight space is automatically adjusted in response to changes in the e
rror surface (i.e., DBD and EDBD) is better than that obtained when predete
rmined step sizes are used (i.e., GD and NCD). However, the reverse applies
when the best forecasts of the 30 trials are considered. The results obtai
ned indicate that the EDBD algorithm is the most parsimonious and the MP al
gorithm is the least parsimonious. It was found that any impact different l
earning rules have on training speed is masked by the effect of epoch size
and the number of hidden nodes required for optimal model performance.