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While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coup ...
In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition ...
In this Master thesis we explore the convex integration method by S. Müller and V. Šverák and its applications to partial differential equations. In particular, we use it to build very irregular solutions to elliptic systems. We also apply this method to b ...
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial differential equ ...
Laser polishing (LP) is a process that allows a significant reduction of the surface roughness of a metal workpiece via re-melting a shallow layer of material. However, the practical use of LP is limited due to the difficulty of satisfying the high surface ...
This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...
In this paper we provide a novel and simple algorithm, Clairvoyant Multiplicative Weights Updates (CMWU), for convergence to \textit{Coarse Correlated Equilibria} (CCE) in general games. CMWU effectively corresponds to the standard MWU algorithm but where ...
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...
Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...
Stabilized explicit methods are particularly efficient, for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they lose their efficiency when a severe stiffness is induced by very few "fast" de ...
