teaching
classes, workshops, and teaching material
PhD in Computer Science, Unversità di Bolzano/Bozen
Physics-Informed Neural Networks and Neural Operators (A.A. 2025/26)
Spring 2026: Guest Lecturer
- Graduate-level introduction to PINNs and Neural Operators. Course Page at UniBz.
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, 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 lecture slides, notebooks and other utilities: DOI: 10.15161/oar.it/qgy53-gk347
GitHub repository containing the Hands-on code: PINN_Course_2026
The Lecture Notes draft is freely available: Download PDF (38Mb) - 1. General Introduction to the course: Motivation, Recaps of Mathematical Analysis, Functional Analysis, Montecarlo Integration (2h30m): slides
09:00 -- 11:30, April 13, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - 2. Intro to numerical resolution of Differential Equations (1h30m): slides
13:00 -- 14:30, April 13, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - Hands-On 1. Finite Difference Method for PDE resolution in Python (1h30): code w/ exercises
09:00 -- 10:30, April 14, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - 3. Introduction to Physics Informed Neural Networks - forward and backward problems (1h30m): slides
09:30 -- 12:30, April 14, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - Hands-On 2. Solving Heat and Burgers equations with PINNs (2h): code w/ exercises
10:00 -- 12:00, April 15, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - 4. Advanced PINNs methods - Learning strategies, Architectures, Losses, and other approaches (3h): slides
14:00 -- 17:00, April 15, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - Hands-On 3. Introduction to PhysicsNeMo for PINNs (1h30): code w/ exercises
09:00 -- 10:30, April 16, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - Hands-On 4. Advanced methods in PhysicsNeMo (1h30): code w/ exercises
13:00 -- 14:30, April 16, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - 5. Neural Operators (3h): slides
09:00 -- 12:00, April 17, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ). - Hands-On 5. Advanced methods in PhysicsNeMo (2h): code w/ exercises
14:00 -- 16:00, April 17, 2026. Aula BZ N-B1.2.11, Via Bruno Buozzi, 1, 39100 Bolzano (BZ).
| Date | Start | End | Duration | Lecture |
|---|---|---|---|---|
| 13/04/2026 | 9:00 | 11:30 | 2h 30m | Fr1. Intro & Prerequisites |
| 13:00 | 14:30 | 1h 30m | Fr2. Intro to numerical PDEs | |
| 14/04/2026 | 9:00 | 10:30 | 1h 30m | Ho1. FDM on PDEs with Python |
| 13:00 | 14:30 | 1h 30m | Fr3. Intro to PINN | |
| 15/04/2026 | 10:00 | 12:00 | 2h 00m | Ho2. solving Heat Equation with PINN |
| 14:00 | 17:00 | 3h 00m | Fr4. Advanced PINNs | |
| 16/04/2026 | 9:00 | 10:30 | 1h 30m | Ho3. Intro to PhysicsNemo-SYM |
| 13:00 | 14:30 | 1h 30m | Ho4. Advanced methods in PhysicsNemo | |
| 17/04/2026 | 9:00 | 12:00 | 3h 00m | Fr5. Neural Operators |
| 14:00 | 16:00 | 2h 00m | Ho5. Darcy Flow with FNO & DeepONet |
PhD in Smart Computing, Unversità di Firenze
Numerical resolution of Differential Equations for applications using Physics-Informed Neural Networks (A.A. 2024/25)
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
Numerical resolution of Differential Equations for applications using Physics-Informed Neural Networks (A.A. 2023/24)
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
Lectures
Lecture held within the UniFi course "ML for Physicists"
Lecturer
- December, 4th, 2025, (Firenze).2 hours
Title: Computer Vision for Nuclear Imaging data on Pictorial Artworks
Slides.
Hackathons
ML-INFN Hackathons. Advanced Level
Lecturer
- November, 15th, 2023, (Pisa, INFN section) Agenda: link.5° Edition
Title: Introduction to solving differential equations with machine learning
Slides. GitHub repo with notebooks.
ML-INFN Hackathons. Base Level
Lecturer
- June, 22th, 2023, (Online) Agenda: link.4° Edition
Title: Real applications of ML in INFN activities - Image Restoration in heritage
GitHub repo with notebooks. - December, 14th, 2021, (Online) Agenda: link.2° Edition
Title: ML Basics: Real applications of ML in INFN activities - Image Restoration in heritage.
GitHub repo with notebooks. Mp4 recording. - June 08th, 2021, (Online) Agenda: link.1° Edition
Title: ML Basics: Real applications of ML in INFN activities - Image Restoration in heritage.
GitHub repo with notebooks. Mp4 recording.