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Welcome to the PINN_PDE wiki!

This project is conducted under the guidance of prof. Sathesh Mariappan from the dept. of Aerospace Engineering at IIT Kanpur. Most of the work at the first commit stage has been carried by Krishna Chaitanya Vaddepally, [MTech] dept. of Aerospace Engg. And further developments are being carried out by Mubashshir Uddin (@meandme234), [BS] dept. of Physics. The project is expected to bear fruit till the end of Summer term 2021(July) and is being carried out in an online setting.

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The project aims to deploy Supervised deep learning frameworks to solve Physical problems, that have time and time proven to be very hard to solve analytically. This is expected to be achieved by the Help of Physics Informed Neural Networks (PINN's) which were first introduced by M Raissi, P Perdikaris, and GE Karniadakis in 2017 https://doi.org/10.1016/j.jcp.2018.10.045 with this pioneering work. Deep learning algorithms are perfect universal function approximators, exploiting this property with a carefully crafted loss function gives us the capability to solve almost any Physical equations numerically. Some of the problematic equations that have been successfully solved using this approach are the Burgers equation, Schrodinger's equation, and Acoustic wave equation (which is currently being analyzed by this project).

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The code utilizes a Tensorflow model to act as the training framework, there are some minor modifications that change the loss function under the light of the Physical problem.