Simulation By Deep Neural Operator (DeepONets)

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