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Physics Informed Neural Networks (PINNs)

Dr.Mohammad Samara

Description

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Description

This is a complete course that will prepare you to use Physics-Informed Neural Networks (PINNs). We will cover the fundamentals of Solving partial differential equations (PDEs) and how to solve them using finite difference method as well as Physics-Informed Neural Networks (PINNs).

What skills will you Learn:

In this course, you will learn the following skills:

  • Understand the Math behind Finite Difference Method .

  • Write and build Algorithms from scratch to sole the Finite Difference Method.

  • Understand the Math behind partial differential equations (PDEs).

  • Write and build Machine Learning Algorithms to solve PINNs using Pytorch.

  • Write and build Machine Learning Algorithms to solve PINNs using DeepXDE.

  • Postprocess the results.

  • Use opensource libraries.

We will cover:

  • Finite Difference Method (FDM) Numerical Solution 1D Heat Equation.

  • Finite Difference Method (FDM) Numerical Solution for 2D Burgers Equation.

  • Physics-Informed Neural Networks (PINNs) Solution for 1D Burgers Equation.

  • Physics-Informed Neural Networks (PINNs) Solution for  2D Heat Equation.

  • Deepxde  Solution for 1D Heat.

  • Deepxde  Solution for  2D Navier Stokes.

If you do not have prior experience in Machine Learning or Computational Engineering, that's no problem. This course is complete and concise, covering the fundamentals of Machine Learning/ partial differential equations (PDEs) Physics-Informed Neural Networks (PINNs). Let's enjoy Learning PINNs together.

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What's inside

Learning objectives

  • Understand the theory behind pdes equations solvers.
  • Build numerical based pdes solver.
  • Build pinns based pdes solver.
  • Understand the theory behind pinns pdes solvers.

Syllabus

Introduction

https://www.youtube.com/@Dr.Mohammad_Samara

Installing Anaconda
Course Structure
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Pytorch Basics
Deep Learning Theory
PyTorch Tensors Basics
Tensors to NumPy arrays
Backpropagation Theory
Backpropagation using PyTorch
FDM Numerical Solution 1D Heat Equation
Numerical solution theory
Pre-processing
Results Evaluation
Solving the Equation
Set Boundary Conditions
Post-processing
PINNs Solution for 2D Heat Equation
FDM Numerical Solution for 2D Burgers Equation
PINNs Solution for 1D Burgers Equation
PINNs Theory
Define the Neural Network
Initial Conditions and Boundary Conditions
Loss Function
Train the Model
Optimizer
Deepxde Solution for 1D Heat
Set Geometry, B.C and I.C
Define the Network and the PDE
Train the model
Result evaluation
Deepxde Solution for 2D Navier Stokes
Set Geometry

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Covers the fundamentals of solving partial differential equations (PDEs) using finite difference method
Provides hands-on experience in building and training Physics-Informed Neural Networks (PINNs) using Pytorch and DeepXDE
Includes real-world examples and case studies, making the learning process more engaging and relevant
Taught by Dr. Mohammad Samara, an expert in the field with extensive research experience in PINNs
Requires prior knowledge in Machine Learning and Computational Engineering, limiting accessibility for beginners
May require additional resources and support for learners with limited mathematical background

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Physics Informed Neural Networks (PINNs) with these activities:
Review Differential Equations
Reviewing differential equations before taking this course will help you to refresh your knowledge of the subject and better prepare you for success.
Browse courses on Differential Equations
Show steps
  • Review your notes from a previous differential equations course.
  • Work through practice problems to test your understanding.
  • Watch online videos or tutorials on differential equations.
Participate in a Study Group
Participating in a study group with other students taking the course will provide you with opportunities to discuss the material, ask questions, and learn from others.
Show steps
  • Find or create a study group with other students in the course.
  • Meet regularly to discuss the course material.
  • Work together on practice problems and projects.
Solve Practice Problems in FDM
Completing practice problems in the Finite Difference Method will help you strengthen your understanding of the concepts and improve your problem-solving skills.
Browse courses on Finite Difference Method
Show steps
  • Review the theory behind the Finite Difference Method.
  • Work through the practice problems provided in the course materials.
  • Check your answers against the provided solutions.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Follow Tutorials on DeepXDE
Following tutorials on DeepXDE will help you learn how to use this framework to solve partial differential equations using PINNs.
Show steps
  • Find tutorials that cover the specific features of DeepXDE that you are interested in.
  • Follow the tutorials step-by-step.
  • Experiment with the different features of DeepXDE.
Develop a Python Script to Solve a PDE Using FDM
Developing a Python script to solve a partial differential equation using the Finite Difference Method will help you to develop your programming skills and your understanding of numerical methods.
Browse courses on Python Programming
Show steps
  • Choose a simple PDE to solve.
  • Implement the Finite Difference Method in Python.
  • Solve the PDE using your Python script.
  • Visualize the solution.
Create a Visual Representation of PINNs
Creating a visual representation of Physics-Informed Neural Networks (PINNs) will help you deepen your understanding of how they work and how they can be used to solve partial differential equations.
Show steps
  • Choose a specific PINN architecture and equation to visualize.
  • Use a tool or library to create a visual representation of the PINN.
  • Present your visualization to your classmates or colleagues.
Create a Course Summary
Creating a course summary will help you to organize and review the material covered in the course.
Show steps
  • Review your notes and handouts.
  • Summarize the key concepts and ideas in each module.
  • Organize your summary in a logical way.
Build a PINN Model for a Real-World Problem
Building a PINN model for a real-world problem will allow you to apply your knowledge and skills to a practical problem, which will help you to solidify your understanding and develop your problem-solving abilities.
Browse courses on Real-World Problems
Show steps
  • Identify a real-world problem that can be solved using a PINN.
  • Collect the necessary data.
  • Build and train a PINN model to solve the problem.
  • Evaluate the performance of the model and make improvements as necessary.
  • Present your findings in a report or presentation.

Career center

Learners who complete Physics Informed Neural Networks (PINNs) will develop knowledge and skills that may be useful to these careers:

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Course image
Effort
7 total hours
Via
Udemy
Instructor
Dr.Mohammad Samara
Language
English
Good to know
Covers the fundamentals of solving partial differential equations (PDEs) using finite difference method
Provides hands-on experience in building and training Physics-Informed Neural Networks (PINNs) using Pytorch and DeepXDE
Includes real-world examples and case studies, making the learning process more engaging and relevant
Taught by Dr. Mohammad Samara, an expert in the field with extensive research experience in PINNs
Requires prior knowledge in Machine Learning and Computational Engineering, limiting accessibility for beginners
May require additional resources and support for learners with limited mathematical background
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