Simulation By Deep Neural Operators (Deeponet)

Model Physical Systems using ONLY DATA

What you'll learn

Understand the Theory behind deep neural operator equations solvers.

Build DeepONet based deep neural operator solver.

Build an deep neural operator code using DeepXDE.

Build an deep neural operator code using Pytorch.

Requirements

High School Math

Basic Python knowledge

Description

This comprehensive course is designed to equip you with the skills to effectively utilize Simulation By Deep Neural Operators. We will delve into the essential concepts of solving partial differential equations (PDEs) and demonstrate how to build a simulation code through the application of Deep Operator Network (DeepONet) using data generated by solving PDEs with the Finite Difference Method (FDM).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 build Simulation code By Deep Neural Operators using Pytorch.Write and build Machine Learning Algorithms to build Simulation code By Deep Neural Operators using DeepXDE.Compare the results of Finite Difference Method (FDM) with the Deep Neural Operator using the Deep Operator Network (DeepONet).We will cover:Pytorch Matrix and Tensors Basics.Finite Difference Method (FDM) Numerical Solution for 1D Heat Equation.Deep Neural Operator to perform integration of an Ordinary Differential Equations(ODE).Deep Neural Operator to perform simulation for 1D Heat Equation using Pytorch.Deep Neural Operator to perform simulation for 1D Heat Equation using DeepXDE.Deep Neural Operator to perform simulation for 2D Fluid Motion using DeepXDE.If you lack prior experience in Machine Learning or Computational Engineering, please dont worry. as this course is comprehensive and course, providing a thorough understanding of Machine Learning and the essential aspects of partial differential equations PDEs and Simulation By Deep Neural Operators by applying Deep Operator Network (DeepONet) . Let's enjoy Learning PINNs together

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Installing Anaconda

Lecture 3 Course structure

Lecture 4 Deep Neural Operator

Section 2: Pytorch Basics

Lecture 5 Deep Learning Theory

Lecture 6 Install PyTorch / CUDA

Lecture 7 PyTorch Tensors Basics

Lecture 8 Tensors to NumPy arrays

Lecture 9 Backpropagation Theory

Lecture 10 Backpropagation using PyTorch

Section 3: FDM Numerical Solution 1D Heat Equation

Lecture 11 Numerical solution theory

Lecture 12 Pre-processing

Lecture 13 Solving the Equation

Lecture 14 Post-processing

Section 4: ODE Integration Neural Operator using PyTorch

Lecture 15 Data creation

Lecture 16 Data Preprocessing - Part 1

Lecture 17 Data Preprocessing - Part 2

Lecture 18 Model Build Up

Lecture 19 Training Process

Lecture 20 Results Evaluation

Section 5: 1D Heat Equation Neural Operator using PyTorch

Lecture 21 Data creation

Lecture 22 Data Preprocessing - Part 1

Lecture 23 Data Preprocessing - Part 2

Lecture 24 Model Build Up

Lecture 25 Training Process

Lecture 26 Results Evaluation

Section 6: 1D Heat Equation Neural Operator using DeepXDE

Lecture 27 Data creation

Lecture 28 Data Preprocessing

Lecture 29 Model Build Up

Lecture 30 Training Process

Lecture 31 Results Evaluation

Section 7: 2D Fluid Neural Operator using DeepXDE

Lecture 32 Data creation

Lecture 33 Data Preprocessing

Lecture 34 Model Build Up

Lecture 35 Training Process

Lecture 36 Results Evaluation

Engineers and Programmers whom want to Learn to perform simulation via a deep neural operator