🎓 Seminar on Uncertainty Quantification and Sensitivity Analysis (UQSA)

Methods and Applications

Time and place: Politecnico di Milano (PoliMi), Milan, Italy February 3–4, 2026

This page is the main entry point to the UQSA seminar, collecting the agenda, lecture slides, and interactive Jupyter notebooks.

Format: Lectures combined with hands-on sessions using interactive Jupyter notebooks (local execution and Google Colab).

🚀 Start here

• 🗓️ Seminar agenda
• 📊 Lecture slides (intro)
• 📊 Summary day one
• 💻 Interactive notebooks – overview below (run locally in JupyterLab or open directly in Google Colab)

📘 Notebook overview

Notebooks are ordered according to the seminar flow, starting from fundamental concepts and progressing to advanced methods and applications.

Preliminaries

• GitHub: preliminaries.ipynb
• Colab: open in Google Colab
  Presents the statistical relations and laws needed to derive the Sobol indices.

Introduction to sensitivity analysis

• GitHub: sensitivity_introduction.ipynb
• Colab: open in Google Colab

Monte Carlo methods for UQSA

• GitHub: monte_carlo.ipynb
• Colab: open in Google Colab

Higher-order sensitivity indices (interaction model)

• GitHub: sensitivity_higher_order.ipynb
• Colab: open in Google Colab
  Demonstrates second- and higher-order (interaction) Sobol indices, compares analytical results with Monte Carlo and polynomial chaos, and discusses convergence and computational cost.

Polynomial chaos expansion methods for UQSA

• GitHub: introduction_gpc.ipynb
• Colab: open in Google Colab

UQSA of arterial wall models

• GitHub: wall_models.ipynb
• Colab: open in Google Colab

UQSA of the g*-function

• GitHub: gstar_function.ipynb
• Colab: open in Google Colab

Exercises

• without solutions
  • GitHub: exercises.ipynb
  • Colab: open in Google Colab
• with solutions
  • GitHub: exercises_with_solutions.ipynb
  • Colab: open in Google Colab