A systematic approach to extracting multivariate polynomial models from neural networks

This study develops a systematic approach to extract multivariate polynomial models from neural networks. A neural network is trained using a random dataset generated using a bivariate polynomial. Numerical values obtained from simulating the neural network are used to estimate the partial derivatives with respect to each input variable with increasing order of partial differentiation until the derivatives become zero. In that way the highest power required in the model is identified for each input variable. A general form of the multivariate polynomial model is written with all possible combinations of powers of the input variables. An appropriate set of corresponding partial differential operators is identified so as to produce a system of partial differential equations from the general polynomial model. The corresponding partial derivatives are estimated numerically and substituted into the equations. On solving the equations, it was found that the method correctly estimates the appropriate parameters for the multivariate polynomial model.