Scientific ML Workshop: Physics-Informed Neural Networks and Neural Operators

25 lis 2023, 10:00 → 9 gru 2023, 15:30 Europe/Warsaw

Room 0.06 (Faculty of Physics, Ludwika Pasteura 5, 02-093 Warszawa, University of Warsaw)

Grzegorz Gruszczyński (University of Warsaw), Marek Bukowicki (University of Warsaw), Szymon Nowakowski (University of Warsaw)

Abstract:

This workshop is an introduction to physics-informed neural networks (PINNs) and neural operators. 

PINNs are a type of machine learning model that can be used to solve partial differential equations (PDEs), which are ubiquitous in physics, engineering, and other fields. PINNs work by embedding the physical laws that govern a given system into the learning process. This allows PINNs to learn accurate solutions to PDEs, even with very spare data.

Neural operators are a more general class of approximators that can be used to learn function-to-function mappings, including those described by PDEs.

Audience:
This workshop is for beginners (students, PhD candidates, academic staff) who have a basic understanding of math, python and machine learning. No prior knowledge of PINNs or Neural Operators is required.

Organizer:
The workshop is organized by:

Center4ML: University of Warsaw

EUROCC2: represented by Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw

The workshop will cover the following topics:

Introduction to the concept of PINNs and Neural Operators

Mathematical foundations of PINNs and Neural Operators

Implementation of PINNs and Neural Operators in Pytorch

Applications of PINNs and Neural Operators in science and engineering
 

Prerequisites:

A laptop + extension cord (PL: przedłużacz)

A Google account to run exercises in Colab

Basic understanding of math (differential equations) and machine learning

Basic understanding of python (numpy)
 

Workshop language:
The workshop will be conducted in English.
This is an in-person (no streaming) event only.

Dates (Saturdays): 25 XI (10:00-13:00), 2 XII (10:00-15:00), 9 XII (10:00-15:00)

Place: Faculty of Physics, Ludwika Pasteura 5, 02-093 Warszawa, University of Warsaw
https://maps.app.goo.gl/WrnrxeCJc3bMZZK48
Room: 0.06 (floor 0)
Plan of the building: http://plany.fuw.edu.pl/pasteura5/floor/0
 

 

Materials will be available in this repository (select the appropriate branch):
 https://github.com/center4ml/Workshops 

Learning Objectives:

By the end of this workshop, you will be able to:

Understand the basics of Physics-Informed Neural Networks (PINNs) and Neural Operators.

Train PINNs to solve engineering problems.

Train Neural Operators to solve a variety of machine-learning tasks.

 

Registration:

The number of places is limited.
The registration deadline is on 10 (Friday) XI 2023.
We will inform about the registration results on 13 (Monday) XI 2023.

We look forward to seeing you!

 

 

sobota, 25 listopada

Day 1 (preliminary, non-obligatory): Preliminaries

Introduction to PyTorch (Szymon Nowakowski)

10:00 - 13:00 Hands-on exercises:
- Writing and running Python in Colab
- Using PyTorch to create and train simple neural networks

Lider: Dr Szymon Nowakowski (University of Warsaw)

Exercises for Day 1

Solutions for Day 1

sobota, 2 grudnia

1 Day 2 (main session)

10:00 - 10:45 Short lecture (Grzegorz Gruszczyński):
- Introduction to Physics-Informed Neural Networks (PINNs)
- The physics-informed loss function

10:45-11:00 break

11:00-11:45 Hands-on exercises (Grzegorz Gruszczyński):
- Training a PINN to solve a simple ODE (mass-spring-damper)

11:45-12:45 lunch break

12:45-15:00 Hands-on exercise (Marek Bukowicki):
- Training a PINN for parameter identification in PDE (heat transfer)

Exercises for Day 2

sobota, 9 grudnia

2 Day 3 (main session)

10:00-10:45 Short Lecture (Grzegorz Gruszczyński)
- Introduction to the concept of Neural Operators
- Architectures: DeepONet, Fourier Neural Operator, ViTO (Vision Transformer Operator)

10:45-11:00 break

11:00-11:45 Hands-on exercises (Szymon Nowakowski):
- Training a Fourier Neural Operator to learn a function-to-function mapping

11:45-12:45 lunch break

12:45-13:30 Hands-on exercise: Understanding a Fourier layer (Szymon Nowakowski)

13:30-13:45 break

13:45-14:30 Hands-on exercise: Training a Fourier Neural Operator to learn a function-to-function mapping (Szymon Nowakowski)

14:30-14:45 break

14:45-15:30 Hands-on exercise: Fighting for super-resolution (Szymon Nowakowski)

Exercises for Day 3