  A virtual chemical spectrophotometer for the simultaneous analysis of nickel
(Ni) and cobalt (Co) was developed based on an artificial neural network (ANN).
The developed ANN correlates the respective concentrations of Co and Ni given
the absorbance profile of a Co-Ni mixture based on the Beer's Law. The virtual
chemical spectrometer was trained using a 3-layer jump connection neural
network model (NNM) with 126 input nodes corresponding to the 126 absorbance
readings from 350 nm to 600 nm, 70 nodes in the hidden layer using a logistic
activation function, and 2 nodes in the output layer with a logistic function.
Test result shows that the NNM has correlation coefficients of 0.9953 and
0.9922 when predicting [Co] and [Ni], respectively. We observed, however, that
the NNM has a duality property and that there exists a real-world practical
application in solving the dual problem: Predict the Co-Ni mixture's absorbance
profile given [Co] and [Ni]. It turns out that the dual problem is much harder
to solve because the intended output has a much bigger cardinality than that of
the input. Thus, we trained the dual ANN, a 3-layer jump connection nets with 2
input nodes corresponding to [Co] and [Ni], 70-logistic-activated nodes in the
hidden layer, and 126 output nodes corresponding to the 126 absorbance readings
from 250 nm to 600 nm. Test result shows that the dual NNM has correlation
coefficients that range from 0.9050 through 0.9980 at 356 nm through 578 nm
with the maximum coefficient observed at 480 nm. This means that the dual ANN
can be used to predict the absorbance profile given the respective Co-Ni
concentrations which can be of importance in creating academic models for a
virtual chemical spectrophotometer.
