DeepXDE Tutorial #1: DeepXDE Setup and Overview | Physics Informed Neural Networks

Video ID - V50 In this comprehensive tutorial, we explore DeepXDE, a Python library for solving a wide variety of differential equations using deep learning with Physics Informed Neural Networks. This video walks you through the process of solving a 1D Poisson equation, from defining the governing differential equation to applying boundary conditions and training a neural network. Key topics covered include: - DeepXDE Setup and Overview - Introduction to the DeepXDE library for solving differential equations. - Setting up the geometry and boundary conditions (Dirichlet conditions) for a 1D domain. - Generating collocation points and preparing training data. - Training a neural network to solve the equation using DeepXDE. - Visualizing the solution with Matplotlib and comparing it to the true solution. - Exploring advanced features like generating animations to visualize training progress. Stay tuned for the next tutorial, where we’ll cover more fundamental topics such as defining governing differential equations, boundary conditions, Hessian, Jacobian etc. Perfect for anyone interested in using machine learning to solve differential equations!