Inverse Physics Informed Neural Networks (I-PINNs) from Udemy

This comprehensive course is designed to equip you with the skills to effectively utilize Inverse Physics-Informed Neural Networks (IPINNs). We will delve into the essential concepts of solving partial differential equations (PDEs) and demonstrate how to compute simulation parameters through the application of Inverse Physics Informed Neural Networks 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 solve Inverse-PINNs using Pytorch.
Write and build Machine Learning Algorithms to solve Inverse-PINNs using DeepXDE.

We will cover:

Pytorch Matrix and Tensors Basics.
Finite Difference Method (FDM) Numerical Solution for 1D Burgers Equation.
Physics-Informed Neural Networks (PINNs) Solution for 1D Burgers Equation.
Total variation diminishing (TVD) Method Solution for 1D Burgers Equation.
Inverse-PINNs Solution for 1D Burgers Equation.
Inverse-PINNs for 2D Navier Stokes Equation 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 Inverse Physics Informed Neural Networks IPINNs.

Let's enjoy Learning PINNs together

What's inside

Learning objectives

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

Understand the theory behind inverse-pinns pdes solvers.
Build an inverse-pinns code solver.

Understand the theory behind pdes equations solvers.
Build numerical based pdes solver.
Understand the theory behind inverse-pinns pdes solvers.
Build an inverse-pinns code solver.

Syllabus

Introduction

Installing Anaconda

Course structure

Pytorch Basics

Deep Learning Theory

Install PyTorch / CUDA

PyTorch Tensors Basics

Tensors to NumPy arrays

Backpropagation Theory

Backpropagation using PyTorch

FDM Numerical Solution for 1D Burgers Equation

Pre-processing

Solving the Equation

Post-processing

Solver Failure!

PINNs Solution for 1D Burgers Equation

PINNs Theory

Define the Neural Network

Initial Conditions and Boundary Conditions

Optimizer

Loss Function

Train the Model

Results Evaluation

TVD Method Solution for 1D Burgers Equation

PINNs VS TVD , Results Comparison

PyTorch: Inverse-PINNs (IPINNs) Solution for 1D Burgers Equation.

Inverse-PINNs Theory

Create The Training Data

Domain Data Input

PINNs VS TVD VS IPINNs , Results Comparison

DeepXDE: Inverse-PINNs for Navier Stokes Equation

Inverse-PINNs Problem Setting

Create The Training Data -Part 1

Create The Training Data -Part 2

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches Inverse Physics Informed Neural Networks IPINNs specifically in PyTorch and DeepXDE

Builds a foundation in partial differential equations and their solutions for engineering

Covers intermediate topics in ML and physics-based ML such as PyTorch tensors, backpropagation, and TVD methods

Requires no advanced experience in ML or computational engineering

Introduces finite difference methods for 1D Burgers, PINNs for 1D Burgers, TVD methods for 1D Burgers, and Inverse-PINNs for 1D Burgers

Covers advanced topics in ML and physics-based ML such as Inverse-PINNs for Navier-Stokes equations using DeepXDE

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 Inverse Physics Informed Neural Networks (I-PINNs) with these activities:

Read 'Introduction to Partial Differential Equations' by K. Sankara Rao

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Develop a strong foundation in Partial Differential Equations

View Numerical Methods For Scientists And Engineers on Amazon

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Read Chapter 1-3 to understand the basic concepts and classification of PDEs.
Solve practice problems to reinforce understanding.
Apply the learned concepts to real-world problems.

Follow tutorials on Pytorch Matrix and Tensors Basics

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Build proficiency in Pytorch basics

Browse courses on PyTorch

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Set up a development environment with Pytorch.
Familiarize with the concepts of matrices and tensors.
Learn how to perform basic operations on matrices and tensors using Pytorch.
Create small programs to apply Pytorch for simple numerical tasks.

Review Calculus

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Strengthen foundational knowledge of Calculus concepts

Browse courses on Calculus

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Review the basics of differentiation and integration.
Solve practice problems involving derivatives and integrals.
Review fundamental theorem of calculus.
Apply calculus to real world problems.

Five other activities

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Solve Finite Difference Method (FDM) practice problems

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Enhance problem-solving skills and reinforce FDM concepts

Browse courses on Finite Difference Method

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Review the basic principles of the Finite Difference Method.
Set up FDM equations for simple problems.
Solve FDM equations using appropriate numerical techniques.
Analyze the accuracy and stability of the FDM solutions.

Attend the next live Q&A session with the course instructor

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Receive clarification and expand understanding during live session

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Submit any questions you have in advance.
Attend the live Q&A session and actively participate.
Take notes of key points and ask follow-up questions.

Create a Python code to solve the 1D Burgers' equation using the Finite Difference Method

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Apply Python skills and enhance understanding of FDM

Browse courses on Python

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Install Python and the necessary libraries.
Implement the Finite Difference Method algorithm in Python for solving the 1D Burgers' equation.
Test and validate the code with different initial conditions and parameters.
Visualize and analyze the numerical solutions obtained.

Solve Inverse PINNs practice problems

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Reinforce understanding of IPINNs through problem solving

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Identify the governing equation for the problem.
Define the input and output data for the IPINNs model.
Train the IPINNs model using appropriate training algorithms.
Validate the trained IPINNs model against known solutions or experimental data.

Create a presentation on the applications of Inverse PINNs

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Expand knowledge of IPINNs and improve presentation skills

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Research various applications of Inverse PINNs in different fields, such as fluid dynamics, heat transfer, and materials science.
Summarize the key concepts and advantages of using IPINNs in these applications.
Design and create a visually appealing presentation using slides and visuals.
Practice delivering the presentation effectively.

Career center

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

Machine Learning Engineer

The field of Machine Learning Engineering has a strong foundation in the concepts taught in this Inverse Physics Informed Neural Networks (I-PINNs) course. As a Machine Learning Engineer, you'll build and utilize Machine Learning models to solve complex problems across various domains. The mathematical underpinnings of PDEs and Inverse-PINNs are crucial in understanding the behavior of physical systems and extracting insights from data. This course provides a comprehensive understanding of these concepts, preparing you to excel in this role.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

Data Science leverages various techniques, including Machine Learning and statistical modeling, to uncover patterns and insights from data. As a Data Scientist, you'll require a solid foundation in solving partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs). This course delves into these concepts, providing you with the necessary skills to analyze and interpret complex datasets, making you a valuable asset in the field of Data Science.

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Computational Scientist

Computational Science combines scientific principles with computational techniques to solve complex problems. As a Computational Scientist, you'll develop and apply numerical methods, including Finite Difference Method (FDM) and Inverse Physics Informed Neural Networks (I-PINNs), to simulate and model physical phenomena. The hands-on approach of this course in building numerical PDE solvers and Inverse-PINNs code will provide you with the essential skills to excel in this field.

See salaries and explore the career path for Computational Scientist

Research Scientist

Research Scientists contribute to the advancement of knowledge in various scientific disciplines. As a Research Scientist specializing in Machine Learning or Computational Science, a deep understanding of Inverse Physics Informed Neural Networks (I-PINNs) is invaluable. This course provides a solid foundation in the theory and application of I-PINNs, enabling you to conduct cutting-edge research and contribute to the development of innovative solutions.

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Software Engineer

Software Engineers design, develop, and maintain software systems. While this course is not directly related to Software Engineering, it may provide valuable insights into the mathematical and computational aspects of software development. The concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) are relevant to certain domains of software engineering, such as scientific computing and data analytics.

See salaries and explore the career path for Software Engineer

Quantitative Analyst

Quantitative Analysts utilize mathematical and statistical models to analyze financial data. While this course does not focus on financial applications, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) are applicable in certain areas of Quantitative Finance, such as risk management and portfolio optimization. This course may provide a foundation for understanding the mathematical underpinnings of these applications.

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Data Analyst

Data Analysts collect, process, and analyze data to extract meaningful insights. This course may be helpful for Data Analysts who wish to specialize in scientific or engineering domains, as it provides a foundation in solving partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs). These concepts are relevant in fields such as computational fluid dynamics, heat transfer, and structural analysis.

See salaries and explore the career path for Data Analyst

Business Analyst

Business Analysts help organizations improve their operations and decision-making by analyzing data and identifying areas for improvement. While this course is not directly related to Business Analysis, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may provide a foundation for understanding complex systems and data patterns in certain business contexts.

See salaries and explore the career path for Business Analyst

Project Manager

Project Managers oversee the planning, execution, and completion of projects. This course may be useful for Project Managers who work in scientific or engineering domains, as it provides insights into the technical aspects of project management. The concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may be relevant in certain project management contexts, such as resource allocation and risk assessment.

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Technical Writer

Technical Writers create and maintain documentation for technical products and services. While this course is not directly related to Technical Writing, it may provide valuable insights into the technical concepts and terminology used in scientific and engineering fields. The concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may be relevant for writing documentation in certain domains.

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Science Teacher

Science Teachers educate students in the field of science. While this course is not directly related to teaching, it may provide a deeper understanding of the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs). This knowledge may be beneficial for Science Teachers who wish to specialize in physics or engineering education.

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Sales Engineer

Sales Engineers provide technical expertise to customers and help them understand and purchase products and services. While this course is not directly related to Sales Engineering, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may be useful for Sales Engineers who work in technical domains, such as scientific equipment or software.

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Financial Analyst

Financial Analysts provide financial advice and guidance to individuals and organizations. While this course is not directly related to Financial Analysis, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may be useful for understanding certain financial models and risk assessment techniques.

See salaries and explore the career path for Financial Analyst

Investment Analyst

Investment Analysts research and evaluate investments to make recommendations to clients. While this course is not directly related to Investment Analysis, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may provide some insights into financial modeling and risk management.

See salaries and explore the career path for Investment Analyst

Risk Analyst

Risk Analysts identify, assess, and manage risks for organizations. While this course is not directly related to Risk Analysis, the concepts of partial differential equations (PDEs) and Inverse Physics Informed Neural Networks (I-PINNs) may provide some insights into risk assessment and modeling techniques.

See salaries and explore the career path for Risk Analyst

Inverse Physics Informed Neural Networks (I-PINNs)

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