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UID:6aab005eaa2b22d43853a05dc86b9f77
CATEGORIES:Special Colloquium
CREATED:20211206T105651
SUMMARY:A Measure Perspective on Uncertainty Quantification
LOCATION:Zoom
DESCRIPTION:Abstract: In many scientific areas, deterministic models (e.g., differentia
 l equations) use numerical parameters. In real-world settings, however, suc
 h parameters might be uncertain or noisy. A more comprehensive model should
  therefore provide a statistical description of the quantity of interest. U
 nderlying this numerical analysis problem is a fundamental question - if tw
 o "similar" functions push-forward the same measure, would the new resultin
 g measures be close, and if so, in what sense? We will first show how the p
 robability density function (PDF) of the quantity of interest can be approx
 imated. We will then discuss an alternative viewpoint: through Optimal Tran
 sport theory, a Wasserstein-distance formulation of our problem yields a mo
 re robust theoretical framework. \nFinally, we will use similar measure-the
 oretic tools to understand two seemingly unrelated problems - the study of 
 high-dimensional zero-sets, and the analysis of statistical sampling algori
 thms.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract: In many scientific areas, deterministic models (e.g., differen
 tial equations) use numerical parameters. In real-world settings, however, 
 such parameters might be uncertain or noisy. A more comprehensive model sho
 uld therefore provide a statistical description of the quantity of interest
 . Underlying this numerical analysis problem is a fundamental question - if
  two "similar" functions push-forward the same measure, would the new resul
 ting measures be close, and if so, in what sense? We will first show how th
 e probability density function (PDF) of the quantity of interest can be app
 roximated. We will then discuss an alternative viewpoint: through Optimal T
 ransport theory, a Wasserstein-distance formulation of our problem yields a
  more robust theoretical framework. <br />Finally, we will use similar meas
 ure-theoretic tools to understand two seemingly unrelated problems - the st
 udy of high-dimensional zero-sets, and the analysis of statistical sampling
  algorithms.</p>
CONTACT:Amir Sagiv, New York University 
DTSTAMP:20260829T233331
DTSTART;TZID=America/New_York:20211208T113000
DTEND;TZID=America/New_York:20211208T123000
SEQUENCE:0
TRANSP:OPAQUE
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