.. Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. .. Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. .. Contributors: :author: Matthias De Lozzo Introduction to Uncertainty Quantification and Management ========================================================= Operate in an uncertain world ----------------------------- Uncertainty Quantification and Management (UQ&M) is a field of engineering on the rise where several questions arise for the user: - **uncertainty quantification**: how to represent the sources of uncertainties, whether by expert opinion or via data? - **uncertainty propagation**: how to propagate these uncertainties through a model or a system of coupled models? - **uncertainty quantification** (again!): how to represent the resulting uncertainty about the output quantity of interest? - **sensitivity analysis**: how to explain this output uncertainty from the input ones? Are there non-influential sources? Can the others be ordered? - **reliability**: what is the probability that the quantity of interest exceeds a threshold? Conversely, what is the guaranteed threshold for a given confidence level? - **robust optimization**: what would be a *good* design solution in terms of performance (or cost) and constraints satisfaction, in an uncertain world? Rather than looking for the best solution in the worst case scenario, which would lead to a very conservative solution, why not relax the constraints by guaranteeing them in 99% of cases while maximizing an average performance (or minimizing an average cost)? |g| implements several UQ&M key concepts through a dedicated package. Moreover, its class :class:`.ParameterSpace` extends the notion of :class:`.DesignSpace` by defining both deterministic and uncertain variables. It can already be used in a :class:`.DOEScenario` to sample a multidisciplinary system. Moreover, the |g| community is currently working on extending its use to any kind of :class:`.Scenario` for robust MDO purposes (see :ref:`roadmap`) by means of dedicated MDO formulations. The package *uncertainty* ------------------------- .. automodule:: gemseo.uncertainty :noindex: