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SIAM Conference on Uncertainty Quantification (UQ20)

Wednesday – 25.03.2020

14:00

iCal
Tim Reid | North Carolina State University | United States

Florian Schäfer | California Institute of Technology | United States

Takeru Matsuda | Department of Mathematical Informatics, The University of Tokyo | Japan

Alejandro Diaz | University College London | United Kingdom

MS021: Probabilistic Numerical Methods for Differential Equations and Linear Algebra (Part I of II)

Chair(s)
Philipp Hennig (University of Tübingen & Max Planck Institute for Intelligent Systems)

Alejandro Diaz (University College London)

Alejandro Diaz (University College London)

Room:
MW HS 1250

Topic:
Probability Theory for UQ

Form of presentation:
Mini-symposium

Duration:
120 Minutes

In many important inverse problems and engineering computations -e.g. numerical weather prediction, medical tomography, reliability analysis- data are related to parameters of interest through the solution of an ordinary or partial differential equation (DE). To proceed with computation, the DE must be discretised and solved through linear algebra methods. However, such discretisation introduces bias into parameter estimates and can in turn cause conclusions to be over-confident. Probabilistic numerical methods for DEs and linear algebra aim to provide uncertainty quantification in the solution space of the DE to properly account for the fact that the governing equations have been altered through discretisation. In contrast to the worst-case error bounds of classical numerical analysis, the stochasticity in DEs and linear solvers serves as the carrier of uncertainty about discretisation error and its impact. This statistical notion of discretisation uncertainty can then be more easily propagated to later inferences, e.g. in a Bayesian inverse problem. Several such probabilistic numerical methods have been developed in recent years, and the connections and distinctions between these methods are starting to be modelled and understood. In particular, an important challenge is to ensure that such uncertainty estimates are well-calibrated. This minisymposium will examine recent advances in both the development and implementation of probabilistic numerical methods in general.

14:00

Prior Distributions and Test Statistics for the Bayesian Conjugate Gradient Method

14:30

A probabilistic view on sparse Cholesky factorization

15:00

Estimation of ordinary differential equation models with discretization error quantification

15:30

Probabilistic rare-event simulation