Welcome to the journey of mastering DeepXDE, a cutting-edge deep learning library designed for solving differential equations efficiently. At its core, DeepXDE is a Physics Informed Neural Networks (PINNs) library that leverages the power of neural networks to solve problems governed by physics. This unique approach integrates mathematical models (like PDEs and ODEs) directly into neural networks, making it a ground breaking tool for researchers, engineers, and students.
This series is carefully structured into two parts to provide a comprehensive learning experience:
This blog post outlines the tentative curriculum for the series. As we explore and learn together, the curriculum will evolve to include new ideas, feedback, and advanced concepts. By the end of the series, you'll have a solid foundation in PINNs and practical experience solving real-world problems using DeepXDE.
DeepXDE is a specialized library built to solve differential equations through Physics Informed Neural Networks (PINNs). But what exactly are PINNs? (Video Tutorial - 1, Video Tutorial - 2, Video Tutorial - 3 and Video Tutorial - 4)
Neural Networks for Physics:
Neural networks are powerful tools capable of approximating complex functions. PINNs take this capability and integrate physical laws (like PDEs or ODEs) directly into the network’s loss function, ensuring that the solution adheres to the governing equations.
Minimal Data Requirement:
Unlike traditional machine learning, which relies on labelled data, PINNs primarily use the physics of the problem to guide the learning process. This makes them ideal for problems where data is scarce but the underlying physical principles are well-known.
Flexibility:
PINNs, and by extension DeepXDE, can solve diverse problems like fluid dynamics, heat transfer, electromagnetics, and quantum mechanics, among others.
DeepXDE simplifies the process of building and training PINNs, offering tools for defining domains, boundary conditions, and equations, and constructing physics informed loss functions automatically.