A Measure Perspective on Uncertainty Propagation

Amir Sagiv (Columbia U, New York)

May 10. 2022, 15:10 — 16:00

In many scientific areas, deterministic models (e.g., differential equations) use numerical parameters. In real-world settings, however, such parameters might be uncertain or noisy. A more comprehensive model should therefore provide a statistical description of the quantity of interest. While standard analysis treats the approximation of moments, we ask whether the full probability density function (PDF) can be accurately estimated in these settings. Underlying this numerical analysis problem is a fundamental question - if two "similar" functions push-forward the same measure, would the new resulting measures be close, and if so, in what sense? We will first show how the PDFs can be approximated. We will then discuss an alternative viewpoint: through Optimal Transport theory, a Wasserstein-distance formulation of our problem yields a more robust theoretical framework.  

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zurich)
Sara van de Geer (ETH Zurich)
Karen Willcox (U of Texas, Austin)