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# Basics Of Neural Network Analysis

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Neural network analysis can be used to predict the performance characteristics of formulations or multi-step processes -- even when there are a large number of variables with complex interactions.

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### Basics Of Neural Network Analysis

1. 1. BASICS OFNEURAL NETWORK ANALYSIS Multilayer Perceptron Neural Networks Kohonen Neural Networks
2. 2. CONTENTS•  What  is  a  Neural  Network?  •  What  can  it  do  for  me?  •  Advantages  and  Disadvantages  •  Two  Common  Types  of  Neural  Networks   –  Mul?layer  Perceptron     •  A  “black  box”  model  predicts  output  values   –  Kohonen  Classiﬁca?on     •  Experimental  cases  are  classiﬁed  into  groups  •  Training  Neural  Networks
3. 3. What  is  a  Neural  Network?  A  neuron  is  a  func?on,  Y=f(X),  with  input  X  and  output  Y:     X   Y     Y  =  f(X)    Neurons  are  connected  by  synapses.  A  synapse  mul?plies  the  output  by  a  weigh?ng  factor,  W:   X   WY   Z   Y  =  f(X)   Z  =  g(WY)
4. 4. The  func?on  in  a  neuron  can  be  linear  or  nonlinear.  A  typical  nonlinear  func?on  is  the  Sigmoid  func?on:
5. 5. Neural  networks  are  trained  with  cases  •  What  is  a  case?   –  A  case  is  an  experiment  with  one  or  more  inputs   (controlled  variables)  and  one  or  more  outputs  (results  or   observa?ons)   –  Example   •  Inputs:  temp  298°K,  ini?al  concentra?on  1.0  g/l,  ?me  7  days;   Outputs:  ﬁnal  concentra?on  0.9  g/l,  degrada?on  product  0.15  g/l
6. 6. When  a  neural  network  is  “trained”  with  diﬀerent  cases,  the  parameters  of  the  neuronal  func?ons  and  synap?c  weigh?ng  factors  are  adjusted  for  the  best  “ﬁt”:              The  inputs  are  x1  thru  xp.  The  outputs  are  y1  thru  ym.    The  w-­‐values  are  the  synap?c  weigh?ng  factors.  The  u-­‐values  are  sums  of  weigh?ng  factors.
7. 7. What  can  a  neural  network  do  for  me?  •  Analyze  data  with  a  large  number  of  variables  with   complex  rela?onships.  •  Develop  formula?ons  or  mul?-­‐step  processes.  •  Compare  performance  characteris?cs  of  mul?ple   formula?ons  or  processes.  •  Analyze  experimental  data  even  when  data  points  are   missing  or  not  in  a  balanced  design.
8. 8. Advantages  •  No  need  to  propose  a  model  prior  to  data  analysis.  •  Can  handle  variables  with  very  complex  interac?ons.  •  No  assump?on  that  inputs  and  outputs  are  normally   distributed.  •  More  robust  to  noise.  •  No  need  to  pre-­‐determine  important  variables  and   interac?ons  with  a  Design  of  Experiments
9. 9. Disadvantages  •  Need  a  lot  of  data.   –  (Number  of  Training  Cases)  ≈  10  x  (Number  of  Synapses)  •  Output  variables  are  not  expressed  as  analy?c  func?ons  of   input  variables.
10. 10. Training  Kohonen  Neural  Networks     and     Mul?layer  Perceptron  Neural  Networks  •  A  por?on  of  the  cases  are  randomly  selected  to  be   training  cases  –  typically  about  70%.  •  A  por?on  of  the  cases  are  randomly  selected  to  be   veriﬁca?on  cases  –  typically  about  20%.  •  The  remainder  are  test  cases  –  typically  about  10%.
11. 11. Teaching  the  neural  network  with  just  the  training  cases  will  result  in  “over-­‐ﬁeng”  the  data:
12. 12. So,  the  veriﬁca?on  cases  are  added:
13. 13. Then  the  network  is  “retrained”  with  the  veriﬁca?on  cases  and  the  ﬁnal  model  is  the  result:
14. 14. Finally,  the  test  cases  are  used  to  determine  how  well  the  “black  box”  model  predicts  the  outputs.  The  outputs  of  a  Kohonen  Neural  Network  will  be  the  diﬀerent  “classes”  into  which  the  cases  have  been  classiﬁed.  The  outputs  of  a  Mul?layer  Perceptron  Neural  Network  will  be  con?nuous  variables  represen?ng  the  performance  characteris?cs  of  all  the  formula?ons  or  all  the  mul?-­‐step  processes.  (Remember,  each  formula?on  or  process  is  a  “case”.)