This project investigated a deep learning alternative to the computationally expensive eigen-decomposition numerical solvers. I applied this research to multiple case-studies in physics, namely the Ising model and electromagnetic propagation. I have modified the loss function in the back-propagation algorithm to include physics constraints, thus achieving higher accuracies and a better extrapolation power with low computational complexity. I have also investigated the effect of this modification on the loss surface to explain my method’s advantages.