FMS025F

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Probabilistic Numerics

7.5

Ren forskarutbildningskurs

7152 (Matematikcentrum (inst LTH) / Matematisk statistik (LTH))

2024-05-07

Maria Sandsten

Engelska

Vid tillräcklig efterfrågan

Scientific computing needs to deal with hetrogeneous sources of error. Namely, numerical errors and measurement errors. The aim of probabilistic numerics is to develop numerical solvers where the error is quantified probabilistically. This enables the development of computational routines that allow incorporation of numerical and statistical errors seamlessly. The main goal of the course is to
introduce the student to the paradigm of probabilistic numerics. In particular, the course develops the method of translating numerical problems into problems of Bayesian inference. It is then demonstrated how this reformulation of the problem affects the design of the numerical solver.

Reproducing kernel Hilbert spaces, Gaussian processes, Gauss-Markov processes, Bayesian state estimation, Bayesian optimization, Bayesian linear algebra, Bayesian, Bayesian quadrature, differential equation solvers.

be familiar with Gaussian process / Gauss-Markov regression.
be able to explain the connection between classical formulations of numerical problems and the probabilistic approach. In particular, know how formulate numerical problems as Bayesian inference.
understand some of the theoretical analysis of the resulting methods.

formulate numerical problems as Bayesian inference.
describe the Bayesian approach to solving numerical problems.
implement some of the solvers on computer systems.

reflect on the constiutent parts of a probabilistic solver, and how they affect the sovler performance.

Föreläsningar

Seminarier

Projekt

Litteraturkurs som självstudier

Skriftlig rapport

Underkänd, godkänd

Linear Algebra, Gaussian processes, Numerical analysis

 

Recommended literature:

Probabilistic Numerics - Computation as Machine Learning, Philipp Hennig, Michael A. Osborne, Hans Kersting.
Bayesian optimization, Roman Garnett.
Research articles.
Lecture notes.

FMS025F

2024-05-07

Maria Sandsten