Predicting microstructural properties using Neural Network: Backpropagation

I want to predict 3 microstructural properties by training neural network (backpropagation) with cooling rate of a alloy solidifying from a liquid as input and my target values as those 3 properties. I have 50 samples of cooling rate and corresponding 50 X 3 values of properties.

1) How should i set my neural network so that i could train it and reproduce the target results in the output ? 2) Also, i should be able to predict the value at any given cooling rate, obviously within a certain range it would be?

[Greg Heath]

Please show what you have done so far.

Greg

[Raghav]

I simply called nftool which uses trainlm and lets me select the size of hidden layer apart from partitioning the data, and fed the i/p with Cooling rate data [1x50] matrix. Similarly the Targets were provided with the [3 X 50] matrix representing the 50 values of my 3 parameters.

The value of the MSE that i have obtained is mostly in the range of 8 - 30.

I tried to use the values of hidden layer from 4-16, but that didn't help much.

Could you please tell me how should i approach this to get better results?

Raghav

Answer 1

[Greg Heath]

1. The scaling of the target data is unbalanced

 meant  = mean(t')'        % [ 36.5 1.08 -4.38 ]'
 vart      = var(t')'            % [  2.67    0.0012   44.4 ]'

Unbalanced scaling will cause NN training to neglect t(1:2,:)

To mitigate the unbalancing, either scale the variables or weight the targets.

Compare the MSE of the separate outputs to those of 3 separate networks.

Without scaling or weighting I get

 rng(0)
 for i = 1:20   
     net = train(fitnet,x,t);
     MSE(i) = perform(net,t,net(x))
 end
  minMSE    = min(MSE)          % 5.26
  medMSE   = median(MSE)   % 14.2
  meanMSE = mean(MSE)      % 14.3
  stdMSE     = std(MSE)           %  4.98
  maxMSE   = max(MSE)         %22.99

2. The input is not very predictive using a three output net without scaling or weighting.

Hope this helps.

Greg

[Greg Heath]

It is easier to understand the significance of the MSE VALUE by comparing it to that of the Naive classifier with constant output equal to the mean of the targets (MSE00)

[ I N ] = size(x) % [ 1 50 ]

y00 = repmat(mean(t')',1,N);

MSE00 = mse(t-y00) % 15.3

minNMSE = min(MSE/MSE00) % 0.3420

medNMSE = median(MSE/MSE00) % 0.9215

meanNMSE = mean(MSE/MSE00) % 0.9319

stdNMSE = std(MSE/MSE00) % 0.3240

maxNMSE = max(MSE/MSE00) % 1.4950

[Raghav]

Could you explain the below mentioned point as to how i change my weights or scale variables?

''To mitigate the unbalancing, either scale the variables or weight the targets''

thanks

Raghav

[Greg Heath]

help/doc/type

mapstd

mapminmax

train