Approximate the solution of a model for inversion layer quantization effects in deep submicron MOSFETs with feed-forward artificial neural networks (ANNs) is proposed.To realize this,the solution of eigenvalue problems actually need to be considered for differential and integrodifferential operators,using ANNs.To validate the method and verify its accuracy,it is applied to the Schr o ¨dinger equation for the Morse potential problem that has an analytically known solution.Then a model is proceeded with which approximates the Schr o ¨dinger equation and the Poisson equation problem called the triangular-potential approximation.In conclusion,the presented method is simple to implement,and have several verification applications.