rate of order (up to) 1/2. It holds with respect to mean square error convergence, whereas previously such a rate for the stochastic Navier-Stokes equations was only known with respect to convergence in p
may not be used to numerically solve PDEs in high dimensions (such as the Fokker-Planck equation) - due to the curse of dimensionality. In such cases, probabilistic methods are preferred, that lead to (stopped) […] proofs equally apply to elliptic and parabolic PDEs, and require a minimum of assumptions on data (such as domains, or involved general second order operators). This is joint work with Fabian Merle (Universität
and additional unstructured effects modeled through a (deep) neural network. To better understand such use cases from a statistical perspective, it is important to address open challenges that exist even […] simpler model class of structured regression models trained in a neural network. This includes aspects such as sparsity, smoothing, and statistical inference, which I will discuss in more detail. Bereits ab
indices. It allows us to also recover various global-in-time $\mathrm{L}^q$-maximal regularity results, such as, for example, an $\mathrm{L}^1_t(\dot{\mathrm{B}}^{s}_{p,1})$ result, which can be of central interest
Vortrag werden Studien dazu vorgestellt, die die Verstehensillusion nach Erklärvideos empirisch untersucht haben und Strategien diskutiert, damit produktiv umzugehen. Bereits ab 16:30 Uhr gibt es für alle
We will discuss the optimal convergence rate and derive a quantitative central limit theorem for such SPDEs. The results can be applied, in particular, to the convergence in the mean-field scaling of
fractional Sobolev spaces $\H^{s}(\mathbb{R}^n)$. Equivalent characterizations with different norms, such as through Littlewood-Paley decompositions or finite differences (Sobolev-Slobodeckij/Gagliardo norms)
Vortrag sollte für alle Mathematik-Interessierten zugänglich sein. Allerdings bietet er erhebliches Suchtpotential, da mehr Fragen offenbleiben als beantwortet werden. Bereits ab 16:30 Uhr gibt es für alle I
The algorithmic advancements are demonstrated for model problems such as the heat equation as well as benchmarks in porous media such as a three-dimensional footing problem. Bereits ab 16:30 Uhr gibt
ed functions in L^1 fulfilling a co-canceling differential condition. This work demonstrates that such a property is not just peculiar to the space L^1. Indeed, under the same differential constraint, […] canceling differential operators are offered for general families of rearrangement-invariant spaces, such as the Orlicz spaces and the Lorentz-Zygmund spaces. Especially relevant instances of inequalities
