Nvidia Modulus: Advanced Topics

Advanced Simulations with AI

What you'll learn

I-PINNs for 2D heat sink flow problem .

DeepONet for  Integration problem.

Fourier Neural Operator FNO for  Darcy problem.

PINNs for  3D Linear Elasticity Problem.

PINNs for  3D Fluid/ Solid Multi Domain Calculation.

PINNs for 3D Geometric Optimization for Heat Exchanger Flow Problem.

Requirements

High School Math

Basic Python knowledge

Description

DescriptionThis course is related with Advanced topics related with PINNs using NVIDIA Modulus. We will cover the topics of Inverse PINNs, Deep Neural Operator Network with DeepONet, Deep Neural Operator Network using Fourier Neural Operator (FNO), PINN for 3D Linear Elasticity Problem, PINNs for Multi Domain Calculation, and Geometric Optimization using PINNs.What skills will you Learn:In this course, you will learn the following skills:Understand the Math behind solving partial differential equations (PDEs) with PINNs, I-PINNs,  Deep Neural Operator Network for DeepONet, along with FNO, Multi Domain Calculation and finally Geometric Optimization using PINNs.Write and build Machine Learning Algorithms to solve PINNs using Nvidia Modulus.Postprocess the results.Pre-process the data and upload it to Nvidia Modulus.Use opensource libraries.We will cover:Inverse Physics-Informed Neural Networks (I-PINNs) Solution for 2D heat sink flow problem .Deep Neural Operator Network (DeepONet) Solution for  Integration problem.Deep Neural Operator Network Fourier Neural Operator (FNO) Solution for  Darcy problem.Physics-Informed Neural Networks (PINNs) Solution for   3D Linear Elasticity Problem.Physics-Informed Neural Networks (PINNs) Solution for   3D Fluid/ Solid Multi Domain Calculation.Physics-Informed Neural Networks (PINNs) Solution for 3D Geometric Optimization for Heat Exchanger Flow Problem.If you do not have prior experience in Machine Learning or Computational Engineering, that's no problem. However it is recommended to have knowledge in the basics of the use and code running using Nvidia Modulus. Let's enjoy Learning Nvidia Modulus together.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Course Structure

Section 2: Inverse PINNs

Lecture 3 Inverse PINNs Theory

Lecture 4 Define the Problem

Lecture 5 Define the Data

Lecture 6 Define the Config File

Lecture 7 Import Needed Libraries

Lecture 8 Define the Governing Equation

Lecture 9 Define the Deep Neural Network

Lecture 10 Add the Data

Lecture 11 Add Inverse Value Monitor

Lecture 12 Solve

Lecture 13 Results Post Processing

Section 3: Deep Neural Operator (DeepONet)

Lecture 14 Deep Neural Operators Theory

Lecture 15 Define the Problem

Lecture 16 Define the Data

Lecture 17 Define the Config File

Lecture 18 Import Needed Libraries

Lecture 19 Define the Deep Neural Network

Lecture 20 Load the Data

Lecture 21 Add the Data Constraint

Lecture 22 Add Results Validator

Lecture 23 Solve

Lecture 24 Results Post Processing

Section 4: Deep Neural Operator (FNO - Fourier Neural Operator)

Lecture 25 Fourier Neural Operator (FNO) Theory

Lecture 26 Darcy Flow Problem

Lecture 27 Define the Config File

Lecture 28 Import Needed Libraries

Lecture 29 Define the Data

Lecture 30 Define the Deep Neural Network

Lecture 31 Add the Data Constraint

Lecture 32 Add Validator

Lecture 33 Solve

Lecture 34 Results View

Section 5: 3D Bracket Stress Analysis

Lecture 35 3D Stress Analysis Problem

Lecture 36 Define the Config File

Lecture 37 Import Needed Libraries

Lecture 38 Define the Gov. Eq.

Lecture 39 Define the DNN

Lecture 40 Define the geometry - part a

Lecture 41 Define the geometry - part b

Lecture 42 Define the B.C, Interior Constraints

Lecture 43 Solve

Lecture 44 Results Post Processing

Section 6: PINNs Multi Domain Calculation

Lecture 45 3D Flow Solid Multi Domain Problem

Lecture 46 Flow configuration file

Lecture 47 Define the geometry - part A

Lecture 48 Define the geometry - part B

Lecture 49 Define the geometry - part C

Lecture 50 Flow: Import Needed Libraries

Lecture 51 Flow: Define the Gov. Eq. / DNN

Lecture 52 Flow: Define the B.C, Interior Constraints

Lecture 53 Flow: Add Monitor

Lecture 54 Thermal : configuration file

Lecture 55 Thermal : Import Needed Libraries

Lecture 56 Thermal : Define the Gov. Eq. / DNN

Lecture 57 Thermal : Define the B.C, Interior Constraints

Lecture 58 Run Flow Code

Lecture 59 Run Thermal Code

Lecture 60 Results Review

Section 7: Geometric Optimization using PINNs

Lecture 61 Parameterized 3D Geometry

Lecture 62 Geometry Update

Lecture 63 Flow Network Update

Lecture 64 Thermal Networks Updated

Lecture 65 Run (Retrain All)

Lecture 66 Results view

Engineers and Programmers whom want to Learn PINNs,learn Advanced Topics NVIDIA Modulus