A multi-layer ANN designed to solve a 2D elliptic PDE for detecting material deformations and inhomogeneity.

Project Overview

Performed as a thesis at IIT Kharagpur under Professor Biswanath Banerjee, this computationally heavy research validated a methodology for estimating material deformations and inhomogeneities using partial boundary and domain data. The core challenge was solving a 2D elliptic Partial Differential Equation (the Inverse Cauchy problem), which is notoriously ill-posed.

To solve this, I designed a multi-layer Artificial Neural Network with variable width to provide the highly non-linear kernels necessary for accurate mapping. The study successfully demonstrated an iterative procedure that isolates optimal material constants for the domain through the alternating minimization of a novel mathematical cost functional.