teaching

Winter 2025: Lecturer

• Graduate-level introduction to PINNs. Syllabus.

  All interested students should contact me at my personal mail. Elegible also as a course for the PhD in Physics.

  Summary:

  The goal of the course is to introduce the concept of Physics Informed Deep Neural Networks (PINN), discuss its implementation from scratch in PyTorch and using advanced ad-hoc developed open-source libraries such as nvidia-modulus for addressing real-world problems in various fields (engineering, physics, petroleum reservoir). We discuss recent topics such as Mixture-of-Models, Neural Operators, Physics-Informed Kolmogorov-Arnold Networks and Physics-Informed Computer Vision.

  Exam:

  Option a: Discussion of a research work on the topic, selected by the student and accepted by the instructor; it has to be presented orally with a presentation and with a Git repo offering the students implementation of the code.

  Option b: Resolution of a small research problem discussed jointly with the instructor; presented either orally with a brief presentation or a written essay, and a Git repo.

  Repository with notebooks and other utilities: pandora.infn.it (it is password protected; I'll give it during the course)
• 0. General Introduction to the course: Motivation, Recaps of Mathematical Analysis, Functional Analysis, Montecarlo Integration (1h+1h): slides and code w/ exercises
  09:30 -- 11:30, January 14, 2025. Aula 217, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• [Extra]. Brief Introduction on Deep Learning: Motivation, Learning as optimisation problem, architectures (2h): slides and MLP example code, LeNet example code
  14:30 -- 16:30, January 14, 2025. Aula 220, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 1. Intro to numerical resolution of Differential Equations (1h+1h): slides and exercises code
  09:30 -- 12:30, January 15, 2025. Aula 219, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 2.Introduction to Physics Informed Neural Networks - Part I forward problems (2h+1h): slides and example code exercise code (solution code )
  09:30 -- 12:30, January 16, 2025. Aula 219, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 3. Introduction to Physics Informed Neural Networks - Part II inverse problems and parametric PINNs (2h+1h): slides and exercise data ( exercise solution for Heat equation)
  09:30 -- 12:30, January 20, 2025. Aula 219, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 4. PINN with nVidia modulus - Part I Introduction & custom PDE (2h+1h): slides and code repository
  09:30 -- 12:30, January 22, 2025. Aula 219, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 5. PINN with nVidia modulus - Part II custom geometry & different NN architectures (2h+1h): slides and code repository
  09:30 -- 12:30, January 24, 2025. Aula 219, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• Link to enrollment form: Mirror 1 Mirror 2 (either one of the two is ok)

  Link to Google Drive Course Folder: mirror 1

  Link to Baltig (INFN gitlab) repository: mirror 1

  Useful updated list of relevant papers: Neural PDE Solver

  Useful tutorial to install (old version) nVidia modulus on Colab (not mine): video and colab (colab mirror 2)

  Lectures will be streamed on Discord Invite link to "PINN Course 2024-2025" discord server

Winter 2024: Lecturer

• Graduate-level introduction to PINNs. Syllabus.

  All interested students should contact me at my personal mail

  Summary:

  The goal of the course is to introduce the concept of Physics Informed Deep Neural Networks (PINN), discuss its implementation from scratch in PyTorch and using advanced ad-hoc developed open-source libraries such as nvidia-modulus for addressing real-world problems in various fields (engineering, physics, oil)

  Exam:

  Option a: Discussion of a research work on the topic, selected by the student and accepted by the instructor; it has to be presented orally with a presentation and with a Git repo offering the students implementation of the code.

  Option b: Resolution of a small research problem discussed jointly with the instructor; presented either orally with a brief presentation or a written essay, and a Git repo.

  Repository with notebooks and other utilities: pandora.infn.it (it is password protected; I'll give it during the course)
• 0. Introductory Lecture (1h+1h): slides and code
  09:00-11:00, January, 11, 2024 (Tentative). Aula 005, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 1. Intro to Differential Equations & their numerical solution (1h+1h): slides and code
  09:00-11:00, January, 12, 2024 (Tentative). Aula 117, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 2.Introduction to Physics Informed Neural Networks - Part I forward problems (2h+1h): slides and example code exercise code (solution code )
  09:00-12:00, January, 18, 2024 (Tentative). Aula 005, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 3. Introduction to Physics Informed Neural Networks - Part II inverse problems and parametric PINNs (2h+1h): slides and exercise data (exercise solution for Heat equation)
  09:00-12:00, January, 19, 2024 (Tentative). Aula 005, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 4. PINN with nVidia modulus - Part I Introduction & custom PDE (2h+1h): slides and code repository
  09:00-12:00, January, 25, 2024 (Tentative). Aula 209, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• 5. PINN with nVidia modulus - Part II custom geometry & different NN architectures (2h+1h): slides and code repository
  09:00-12:00, January, 26, 2024 (Tentative). Aula 209, Plesso Didattico Morgagni - viale Morgagni, 44-48, 50134 Firenze (FI).
• Link to enrollment form: Mirror 1 Mirror 2 (either one of the two is ok)

  Link to Baltig (INFN gitlab) repository: mirror 1

  Useful updated list of relevant papers: Neural PDE Solver

  Useful tutorial to install (old version) nVidia modulus on Colab (not mine): video and colab (colab mirror 2)

  Lectures will be streamed on Discord Invite link to discord server

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