Is it possible to create an analytical expression from an artificial neural network toolbox in MATLAB? If not, then how can these datasets be used as objective function in optimization?
In some papers, some arbitrary fitted polynomials are generated (which may be a combination of log, trigonmetric, expotential functions) and some have also claimed that this is the best-fitted expression out of 30 lakhs analytical expressions. How this can be derived??
Thank you in advance
Dear Prasenjit,
welcome!
I would like to give a conceptual answer. Any signal processing system or sub system represented in mat lab must be describable in a mathematical and logical forms. This includes the neural networks.Once you have the configuration of the neural network you can describe its performance in a system of mathematical equations. The unknown system parameters are obtained by the learning algorithms. So, you need to revert to the possible analytical descriptions of the neural networks.
This is not a direct solution of your problem but these principles may guide you to solve your problem.
Neural networks is a machine learning algorithm that learn from a dataset to do a defined task.
for example supervised Neural networks, trying to find relationship between input and output.
This relationship can be linear or nonlinear.
after training , NN learn the relationship. but this knowledge is hidden in its neurons synoptic weights, and I think we can not simply analyze this weights to know the exact equation between input and output.
as you mentioned there is a toolbox in matlab that you can use to know the equation.
you simply fit som linear or nonlinear (polynomial, gaussian, splines) kernels to data to see the relationship between input and output.( the exact equation)
Michael Short Mohammad Norizadeh Cherloo Muhammad Ali
Thank you for your valuable response.
In the attached file there are some arbitrary expressions. How to derive that ??
You can find out the function that has been "learned" by your Neural Net, but it wouldn't be as insightful as you might think. it would be incomprehensible. One should instead conduct an explainability and interpretability analysis of the said Neural network to understand the nature of the mapped function better.
Yes, you can,
See the attachment
Example:
after training the ANN, a model equation was established with the weights as the model parameters. Using the values of the weights and biases , the expression can be written to arrive at a correlation of unconfined compressive strength of treated soils with the input parameters
Dear Prasenjit,
welcome!
I would like to give a conceptual answer. Any signal processing system or sub system represented in mat lab must be describable in a mathematical and logical forms. This includes the neural networks.Once you have the configuration of the neural network you can describe its performance in a system of mathematical equations. The unknown system parameters are obtained by the learning algorithms. So, you need to revert to the possible analytical descriptions of the neural networks.
This is not a direct solution of your problem but these principles may guide you to solve your problem.
Mohamed Abdel-Nasser
Thank you for your comment
is there any paper or article related to this??
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