深度神经算子模拟 (DeepONet)课程 Simulation By Deep Neural Operators (DeepONet)

该课程旨在通过仅使用数据对物理系统进行建模，让学生掌握有效利用深度神经算子模拟的技能。在课程中，学生将了解深度神经算子方程求解器背后的理论，并构建基于DeepONet的深度神经算子求解器。同时，学生将学习使用DeepXDE构建深度神经运算符代码和使用Pytorch构建深度神经运算符代码的技能。

为了适应本课程，学生需要具备高中数学和基本的Python知识。在课程中，学生将深入研究求解偏微分方程（PDE）的基本概念，并演示如何使用有限差分法（FDM）求解偏微分方程（PDE）所生成的数据。通过应用深度算子网络（DeepONet）来构建仿真代码，学生将掌握以下技能：了解有限差分法背后的数学，从头开始编写和构建算法以掌握有限差分法，了解偏微分方程（PDE）背后的数学，编写并构建机器学习算法来构建模拟使用Pytorch通过深度神经算子编写代码，使用DeepXDE通过深度神经算子编写并构建机器学习算法来构建模拟代码。

在本课程中，学生将学习将有限差分法（FDM）的结果与使用深度算子网络（DeepONet）的深度神经算子进行比较。课程还将涵盖Pytorch矩阵和张量基础知识、一维热方程的有限差分法（FDM）数值解、深度神经运算符执行常微分方程（ODE）的积分、深度神经运算符使用一维热方程执行模拟Pytorch、Deep Neural Operator使用DeepXDE执行1D热方程模拟以及Deep Neural Operator使用DeepXDE执行2D流体运动模拟。

如果学生缺乏机器学习或计算工程方面的经验，也不必担心。因为本课程是综合性的课程，通过应用深度算子网络（DeepONet）提供对机器学习以及偏微分方程和深度神经算子模拟的基本方面的透彻理解。本课程将让学生享受学习PINN的乐趣，成为深度神经算子模拟的专家。

由 Mohammad Samara 博士创建
MP4 | 视频：h264，1280×720 | 音频：AAC、44.1 KHz、2 Ch
类型：电子学习 | 语言： 英语 | 持续时间：36 场讲座（8 小时 28 分钟）| 大小：10.6 GB 含课程文件

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