Physics-Informed Neural Networks for Solving Differential Equations
A data-driven approach to solve differential equations
The recent advances in Machine Learning (ML) has seen incredible results in computer vision (CV), time-series prediction, recommendation systems, and natural language processing (NLP). The application of ML to physics especially in solving differential equations has shown considerable developments as well.
This post deals with solving a well-known PDE, used widely in fluid dynamics called “Burger’s Equation” using Physics-Informed Neural Networks (PINNs). Given fixed model parameters, the goal is to learn a data-driven solution to the PDEs. PINNs exploit the automatic differentiation feature of deep learning libraries like “Pytorch” to provide a solution. This is an implementation of this paper. The images used for illustrations have been taken from the same paper.
Why PINNs? Why not traditional NNs?
- Traditional NNs can be used to solve the PDEs. However, they only use the ground truth to learn the solution in a regression setting and do not use the information obtained from the differential equation and boundary conditions. Traditional NNs do not understand physics.
- In the PINN approach, the loss function is formulated so that the NN…
