Physics Informed Neural Network (Pinns)

Simulations with AI

What you'll learn

Understand the Theory behind PDEs equations solvers.

Build numerical based PDEs solver.

Build PINNs based pdes solver.

Understand the Theory behind PINNs PDEs solvers.

Requirements

High School Math

Basic Python knowledge

Description

DescriptionThis 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.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Installing Anaconda

Lecture 3 Course Structure

Section 2: FDM Numerical Solution 1D Heat Equation

Lecture 4 Numerical solution theory

Lecture 5 Pre-processing

Lecture 6 Solving the Equation

Lecture 7 Post-processing

Section 3: FDM Numerical Solution for 2D Burgers Equation

Lecture 8 Pre-processing

Lecture 9 Solving the Equation

Lecture 10 Post-processing

Section 4: PINNs Solution for 1D Burgers Equation

Lecture 11 PINNs Theory

Lecture 12 Deep Learning Theory

Lecture 13 Define the Neural Network

Lecture 14 Initial Conditions and Boundary Conditions

Lecture 15 Optimizer

Lecture 16 Loss Function

Lecture 17 Train the Model

Lecture 18 Results Evaluation

Section 5: PINNs Solution for 2D Heat Equation

Lecture 19 Define the Neural Network

Lecture 20 Initial Conditions and Boundary Conditions

Lecture 21 Optimizer

Lecture 22 Loss Function

Lecture 23 Train the Model

Lecture 24 Results Evaluation

Section 6: Deepxde Solution for 1D Heat

Lecture 25 Set Geometry, B.C and I.C

Lecture 26 Define the Network and the PDE

Lecture 27 Train the model

Lecture 28 Result evaluation

Section 7: Deepxde Solution for 2D Navier Stokes

Lecture 29 Set Geometry

Lecture 30 Set Boundary Conditions

Lecture 31 Define the Network and the PDE

Lecture 32 Train the model

Lecture 33 Result evaluation

Engineers and Programmers whom want to Learn PINNs