Seminar agenda – Global Sensitivity Analysis for Cardiovascular Models

Seminar agenda — UQSA

Organiser: NTNU and Politecnico di Milano (PoliMi)
Dates: 3–4 February 2026
Instructor: Leif Rune Hellevik
Location: Politecnico di Milano, Milan, Italy (Natta-tav)

The seminar is structured over two half-days, combining conceptual framing with guided, notebook-based exploration. The timetable respects the confirmed room reservations.

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Day 1 — Tuesday 3 February 2026

Time: 10:00–15:00

Time	Block	What you do / material
10:00–10:40	GSA for cardiovascular models (Welcome + framing)	Motivation, concepts, and intuition (Lecture slides)
10:40–11:00	Transition: from slides to statistics	Explain why variance is needed for Sobol indices
11:00–11:30	Foundations: variance and total variance	preliminaries.ipynb (selected cells)
11:30–11:45	Coffee break	—
11:45–12:30	What does sensitivity mean in practice?	sensitivity_introduction.ipynb (Part 1)
12:30–13:15	First-order Sobol indices	sensitivity_introduction.ipynb (Part 2)
13:15–14:00	Lunch break	—
14:00–15:00	What is missing in first-order indices?	sensitivity_introduction.ipynb (Part 3: total indices + interactions)

Day 1 — description of blocks

GSA for cardiovascular models (Lecture slides)
Conceptual framing of uncertainty, credibility, and global sensitivity analysis in the context of complex models and digital twins. Introduces key ideas without formulas and sets expectations for the notebook-based format.

Foundations: variance and total variance
Selected parts of preliminaries.ipynb to recall variance and the law of total variance as the statistical foundation for Sobol indices.

Sensitivity in practice (Part 1)
Guided exploration of sensitivity_introduction.ipynb: scatterplots, conditional behaviour, and qualitative intuition about input–output relationships.

First-order Sobol indices (Part 2)
Computation and interpretation of first-order Sobol indices within sensitivity_introduction.ipynb.

What is missing in first-order indices? (Part 3)
Introduction of total Sobol indices and interaction effects within sensitivity_introduction.ipynb.

Outcome of Day 1:
Participants understand what Sobol indices mean and why interactions matter.

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Day 2 — Wednesday 4 February 2026

Time: 10:00–13:00

Time	Block	What you do / material
10:00–10:15	Recap and framing of Day 2	From “what Sobol indices mean” → “how we compute them”
10:15–10:45	Monte Carlo in practice	monte_carlo.ipynb
10:45–11:10	Higher-order effects and interactions	sensitivity_higher_order.ipynb
11:10–11:25	Coffee break	—
11:25–11:55	Polynomial Chaos (PCE) approach	introduction_gpc.ipynb
11:55–12:25	Application I: arterial wall models	wall_models.ipynb
12:25–13:00	Application II: g*-function + wrap-up	gstar_function.ipynb

Day 2 — description of blocks

Recap and framing of Day 2
Short synthesis: Day 1 focused on meaning and intuition; Day 2 focuses on computation and applications.

Monte Carlo in practice
Demonstration of Sobol estimation via Monte Carlo, including sampling cost and convergence.

Higher-order effects and interactions
Exploration of interaction effects and interpretation of total vs. first-order indices.

Polynomial Chaos approach
Comparison of Monte Carlo and PCE: same quantities (variance and Sobol indices), but different efficiency and assumptions.

Application I — arterial wall models
Realistic case study showing which parameters dominate uncertainty in arterial wall predictions and why this matters for credibility.

Application II — g*-function + wrap-up
Benchmark nonlinear example illustrating nonlinearity and interactions, followed by key take-home messages and pointers to materials.

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Practical information

The seminar combines guided demonstration with interactive exploration. Participants who wish to run code will be provided with ready-to-use notebooks and Colab links.

Interactive notebooks and slides will be shared after the seminar.

Familiarity with basic probability and numerical modelling is helpful, but no prior experience with sensitivity analysis is assumed.