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Nonintrusive model order reduction for stochastic differential equations

Autoren: M. A. Freitag, J. M. Nicolaus, M. Redmann (2024)

A non-intrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD.

Zeitschrift:
arXiv

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Universität Potsdam
Institut für Mathematik
Campus Golm, Haus 9
Karl-Liebknecht-Str. 24-25
D-14476 Potsdam

Aktivitäten

22.11.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Matched pairs, post-Hopf algebras and the quantum Yang-Baxter equation

Yunan Li (Guangzhong, China) (online)

Recently, Ferri and Sciandra introduced two equivalent notions, matched pair of actions on a Hopf algebra and Yetter-Drinfeld brace. Any of these objects actually provides a solution of the quantum... 

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27.11. bis 29.11.2024  –  Campus "Am Neuen Palais" Building 8, Seminar room 0.58
Konferenz

QFT Workshop

Analytical methods in interplay with physics

A workshop to explore Asymptotics, Randomness and Noncommutativity

This three day workshop aims at fostering interactions between mathematicians who use... 

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04.12.2024, 13:30 - 14:20 (special session)  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium

Mathematical probability: Why a game-theoretic approach?

Glenn Shafer (Rutgers Business School, Newark)

Most applications of mathematical probability rely, in one way or another, on theorems that give certain events high probability. Since the 1950s, mathematicians have largely agreed that these... 

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05.12.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

The equivariant index theorem with boundary.

Lennart Ronge

Given a Dirac type operator on a manifold with boundary and a group action that preserves all relevant structures, one can define a generalized index for any group element. Analogous to the APS index... 

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06.12.2024, 10:00  –  Campus Golm, Building 9, Room 1.10 and via Zoom
Arbeitsgruppenseminar Analysis

From modular graph forms to iterated integrals (Part 3)

Emiel Claasen (MPI, Potsdam)

Modular Graph Forms (MGFs) are a class of modular forms represented by lattice sums associated to directed simple graphs. They originated from the calculation of graviton amplitudes in type II string... 

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