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Artificial Neural Networks are universal approximators and in this project, I aim to study the effectiveness of ANNs over traditional numerical methods to solve engineering problems. Specifically statics and dynamics of mechanical structures and non linear odes are looked into for applications. This work is based on the book by Prof Snehashish Chakraverty and Dr. Sumit Kumar Jeswal. I aim to validate their claims in the book "Applied Artificial Neural Network Methods for Engineers and Scientists" and also arrive at possible extensions to the methods discussed in the book.