Monday, October 31, 2022
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All day |
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3pm |
10/31/2022 - 3:00pm Abstract: Data-driven models that respect physical laws are robust to noise, require few training samples, and are highly generalisable. Although the dynamic mode decomposition (DMD) is a principal tool of data-driven fluid dynamics, it is rare for learned DMD models to obey physical laws such as symmetries, invariances, causalities, spatial locality and conservation laws. Thus, we present physics-informed dynamic mode decomposition (piDMD), a suite of tools that incorporate physical structures into linear system identification. Specifically, we develop efficient and accurate algorithms that produce DMD models that obey the matrix analogues of user-specified physical constraints. Through a range of examples from fluid dynamics, we demonstrate the improved diagnostic, predictive and interpretative abilities of piDMD. We consider examples from stability analysis, data-driven resolvent analysis, reduced-order modelling, control, and the low-data and high-noise regimes. Location:
AKW 200
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4pm |
10/31/2022 - 4:00pm Let $G$ be a connected semisimple real algebraic group, $K<G$ a maximal compact subgroup, and $\Gamma<G$ a Zariski dense discrete subgroup. We are interested in the distribution of properly immersed maximal flats of a locally symmetric space $\Gamma\backslash G/K$, as well as the distribution of their holonomies (elliptic components of the stabilizer in $\Gamma$). Margulis, Mohammadi, and Oh have shown joint equidistribution of closed geodesics and holonomies in the rank $1$ case when $\Gamma$ is geometrically finite. We show joint equidistribution in higher rank, under an Anosov assumption on $\Gamma$. I will present an overview of our result and the method of proof. Joint work with Michael Chow. Location:
LOM 206
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