Basically you already know the "equation" encoded by your ANN after training. Considering that Y is the output of your network, X the input then ANN are following :

Yj = f( SUM(XiWij) ) with Wij being the connection weight between those two (eventually distributed over several layers) and f() being the activation function of your neuron. Through learning the ANN is just finding the coefficient of your equation in the form of weights.

If you want to go for the litteral approach you have to tune your learning algorithm so that it can deal with the symbols you are using. If what you want to achieve is to give numerical samples to an ANN and then derive the litteral equation of the function that the network learnt, either you do that analytically through development of you network computation (the big equation with weights as coefficients) or you face a very difficult problem. One way to achieve this automatic "literralization" of an arbitrary neural network would be to teach a separate network how to label know functions, ie:

- train a network A to learn a function f(x) that you now in advance, let say Y=X²

- train a second network B using as input the weights of A and as output the litteral expression of f(x)

- repeat the process until B has learnt several functions

Although that would probably imply that you need to find a way to make B as a recursive network that can output a function as a composition of other functions...

Genetic algorithm seem an easier approach, but you are dealing with a difficult issue ;)

I think it is not possible because neural network perform two kind of tasks first regression and second classification , but deriving a formula to satisfy some input - output relation is a matter of arranging operators and operands not weight adjustment. Theoretically like our brain does derive formula for specific patterns, like situation i never encountered practically. So my suggestion is no.

It is possible to obtain an equation after developing an ANN for prediction. If fact, you will end up with a long equation including the inputs, weights, biases, etc.

After the network is well trained you have weights and biases by which you can write the formula.

As was mentioned before by Dr. Ahmadi-Nedushan you will be end up with a very long equation (useless!). Accordingly we leave the results as matrices. If you want a compact equation I suggest you try GP instead.

Hi everyone. I believe one way of creating equations from ANN is first to take the input data with target data and train ANN to create a model which create a relationship between the input and target data. Based on the output predicted by ANN one can create an equation based on the original input and predicted output. The equation is a curve fitting process which can be very complicated equation sometime.

Thank you for the great answers! The problem is predicting logical connectives in fuzzy logics, so from your answers, I think genetic programming would be more appropriate due to producing compact results.

Best regards,

Islam

You can create a NN with a genetic algorithm whose "DNA" codes for the NN architecture (neural activation functions, connection weights and biases). Then, through mutations and cross-overs you evolve the genome to minimize a cost function (e.g. mean squared error).

I used this approach to learn the functional relationship between temperature, ionic abundance, and line emission ratio indicators in galactic planetary nebulae/HII regions:

https://www.researchgate.net/publication/215454690_On_the_Deduction_of_Galactic_Abundances_with_Evolutionary_Neural_Networks?ev=prf_pub

There is a more explanatory description of the process also in a PPT talk I gave here:

https://patternizer.files.wordpress.com/2009/10/2006_stargal.ppt

Hope this helps get you started.

Cheers,

Mike

Conference Paper On the deduction of galactic abundances with evolutionary ne...

@down-votes: it's a voting mechanism, doesn't say some answer is incorrect, just some are better than others. (of course this must not be done systematically based on the poster, but based on quality of the answer)

ANN is basically nonlinear regression model. so after training the data set you will be having some weights and bias. by using theses weights you can develop regression formula

Basically you already know the "equation" encoded by your ANN after training. Considering that Y is the output of your network, X the input then ANN are following :

Yj = f( SUM(XiWij) ) with Wij being the connection weight between those two (eventually distributed over several layers) and f() being the activation function of your neuron. Through learning the ANN is just finding the coefficient of your equation in the form of weights.

If you want to go for the litteral approach you have to tune your learning algorithm so that it can deal with the symbols you are using. If what you want to achieve is to give numerical samples to an ANN and then derive the litteral equation of the function that the network learnt, either you do that analytically through development of you network computation (the big equation with weights as coefficients) or you face a very difficult problem. One way to achieve this automatic "literralization" of an arbitrary neural network would be to teach a separate network how to label know functions, ie:

- train a network A to learn a function f(x) that you now in advance, let say Y=X²

- train a second network B using as input the weights of A and as output the litteral expression of f(x)

- repeat the process until B has learnt several functions

Although that would probably imply that you need to find a way to make B as a recursive network that can output a function as a composition of other functions...

Genetic algorithm seem an easier approach, but you are dealing with a difficult issue ;)

.

you might be interested in reading the attached overview describing how Megaputer's Polyanalist does it

.

Thank you all for your contributions!

Are you looking for something like this http://www.nutonian.com/products/eureqa/ ?

You can use gene expression programming for deriving formulas between input and output data.

Yes. You can derive a physical equation from ANN simulation based on weights and biases. In order to do this, you can check our journal: Abidoye and Mahdi (2014). Or you can mail me for a more explicit  paper that teaches the procedure. ([email protected])

@Abidoye hello I am also working for forecasting and want to develop equation by train In network. Kindly give a procedure with a suitable example. Thanku

@Luqman Abidoye Kindly mail me the same :) ([email protected])

i also have respnses of the displacement in top node in structure obtained from opensees finite element that varies by using two random variable fy and E. I have properties of mean and stdv of random variable. how to predict relation of responses and random variable in form of explicit function. Can i use ann or ga?

@luqman Abidoye, I'm interested to read the paper as mentioned earlier, kindly email me the paper at [email protected]

@luqman abidoye , please mail me at [email protected]

@luqman Abidoye, I'm interested to read the paper as mentioned earlier, kindly email me the paper at [email protected]

@luqman Abidoye, Kindly also email me yours journal on this id [email protected] in anticipation

When the problem is formulated in a symbolic way, it is better Genetic programming.

@luqman abidoye , please mail me at [email protected]

There are also some approaches based on three graphs