- Docente responsabile
- LUCA BONAVENTURA
- CCS proponenti
- Ingegneria Civile per la Mitigazione del Rischio Ingegneria Fisica
- CFU
- 3
- Ore in presenza
- 40
- Prerequisiti
- Basic knowledge of the MATLAB or Python scientific softwares and mathematics knowledge at the Batchelor degree level.
- N° max studenti
- 30
- Criteri di selezione
- Precedence to students enrolled in the courses of Civil Engineering for Risk Mitigation, Physical Engineering, Mechanical Engineering. Evaluation of the weighted average.
- Parole chiave:
- Differential equations, Mathematical modelling, Neural networks
- Tag
- Artificial intelligence, Science, Software
Descrizione dell'iniziativa
General description
The goal of the activity is to introduce advanced approaches to mathematical modelling of physical phenomena that integrate more conventional equation-based models with novel data-driven techniques based on neural networks. This hybridization of classical and innovative techniques is increasingly often employed to complement both approaches and achieve more accurate and efficient mathematical models of complex physical phenomena. More specifically, we will provide a self contained introduction to Physically Informed Neural Networks (PINN), [1],[2],[3] in the case in which the underlying physical model consists of a system of Ordinary Differential Equations (ODE). This will allow to present to the students novel and advanced concepts on data-driven modelling in a framework that is more familiar to them from their curricular activities. Advanced optimization techniques for PINN recently developed by some of the teachers [4] could also be included among the treated topics.
Experimental didactic approach
The activity will consist in 40 hours of class work distributed over two weeks (five days per week), organized according to the flipped classroom concept and streamed online, with a group of students participanting from the ENHANCE partner and students joining online also from different POLIMI campuses. Students will be provided in advance with recorded introductions to the topics to be studied and with a set of lecture notes. During each meeting (four hours per day over two weeks), one hour approximately will be devoted to the discussion of the theoretical topics after the students have first gone through the recorded introduction and a first reading of the course notes on their own. The discussion of key issues and the clarification of individual doubts will be initiated with the help of online tools (Wooclap). The students will then be presented with a set of problems of increasing complexity concerning the discussed topics, to be solved in Python. After an introduction to the specific Python tools required for each task, about half of each meeting will be reserved for programming laboratory activity devoted to the solution of these problems, with the emphasis on the interpretation of the results obtained. In order to guarantee an optimal implementation of the proposed experimental didactic approach, the organization of all the teaching activities will be discussed in close cooperation with METID (POLIMI department for innovative teaching techniques) and METID will also present students with online questionnaires at the beginning and at the end of the activity to monitor the participants reaction and feedback.
Assessment of the students' participation
All students, participating either in the classroom or online, will hand in results within the lecture day through the online system for assignment submission provided by the WeBeep portal at POLIMI. In this way, the students' activity will be continuously monitored by the teachers, reviewing each day their results and formulating a final judgement on their participation.
References
[1] M. Raissi, P. Perdikaris, G. E. Karniadakis, J. Comp. Phys. 378, 686–707, (2019)
[2] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang, Nature Rev. Phys. 3 (6),422–440, (2021)
[3] V. Dolean, A. Heinlein, Mishra, B. Moseley, Comp. Meth. in App. Mech. Engineering, 429,
117116, (2024)
[4] C. Visser, A. Heinlein, B. Giovanardi, arXiv:2411.19632, (2024)
Periodo di svolgimento
dal June 2026 a July 2026
Calendario
29 Giugno 9.00-12.00 (Preliminare di introduzione a Python, questionario iniziale)
29 Giugno 14.00-18.00
30 Giugno 10.00- 12.00 14.00-16.00
1 Luglio 10.00- 12.00 14.00-16.00
2 Luglio 10.00- 12.00 14.00-16.00
3 Luglio 10.00- 12.00 14.00-16.00
6 Luglio 10.00- 12.00 14.00-16.00
7 Luglio 10.00- 12.00 14.00-16.00
8 Luglio 10.00- 12.00 14.00-16.00
9 Luglio 10.00- 12.00 14.00-16.00
10 Luglio 10.00- 12.00 (Conclusioni, questionario finale)