Uncertainty Quantification in Numerical Simulations

École des Ponts ParisTech
LEVEL
Master
TYPE
Course
MODES
-
LANGUAGE
-
ECTS
1.5
PERIOD
18/11/2024 to 22/11/2024

Course Description

Uncertainty quantification is used in analysis and modeling (e.g. sources of uncertainty in a physical system), optimization and operations research (e.g. uncertainties on supply and demand in the modeling of a supply chain), vision and machine learning (processing noisy data…), or quantitative finance (financial risk management…).

Numerical simulation is an essential tool for modeling and analyzing complex systems in many scientific fields (physics, biology, chemistry, finance, economics, etc.). The expectations associated with it are multiple: better identification and control of risks, limitation of the costs of real experiments (car crash tests for example), search for cost-performance trade-offs, etc. The presence of many sources of uncertainty (on the models, their parameters, the reference measurements) nevertheless raises the question of the confidence that can be associated with the decisions and predictions provided by the simulation.

The objective of this course is to present a set of mathematical methods to model, propagate and analyze these uncertainties in numerical simulations.

Subject area

Mathematics

Time format

one-week

Educational-info

Application deadline

15/09/2024

Competences

At the end of the module, students will
– know the theoretical foundations of the usual methods of uncertainty quantification;
– be able to implement these methods (using R) on concrete case studies

Prerequisites

Basic mathematics at final year of bachelor level knowledge in probability and statistics (linear algebra, optimization, cumulative density functions, parametric estimation, limit theorems, confidence intervals).

Duration

1 week

ECTS

1.5

Validation mode

written exam

Maximum number of students

25

Organizer

Partner

École des Ponts ParisTech

Faculty

School of Engineering

Department

Department of Mathematics and Computer Science

Contact or registration links