Zobrazeno 1 - 10
of 74 023
pro vyhledávání: '"MATHEMATICS / Numerical Analysis"'
In this paper, we consider the simplest version of a linear neural network (LNN). Assuming that for training (constructing an optimal weight matrix $Q$) we have a set of training pairs, i.e. we know the input data \begin{equation} G=\left\{g^{\left(1
Externí odkaz:
http://arxiv.org/abs/2408.04871
We introduce a hybrid filter that incorporates a mathematically accurate moment-based filter with a data driven filter for discontinuous Galerkin approximations to PDE solutions that contain discontinuities. Numerical solutions of PDEs suffer from an
Externí odkaz:
http://arxiv.org/abs/2408.05193
Autor:
Daněk, Josef, Pospíšil, Jan
In this paper we numerically analyse problems that arise in numerical integration used in various problems that are nowadays being solved by physics-informed neural networks. In particular we show how inaccurately evaluated integrands can lead to sev
Externí odkaz:
http://arxiv.org/abs/2408.05172
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we obtain a s
Externí odkaz:
http://arxiv.org/abs/2408.05095
We introduce a new implementation of the Immersed Boundary method in the finite-volume library OpenFOAM. The implementation is tailored to the simulation of temperature-dependent non-Newtonian polymeric flows in complex moving geometries, such as tho
Externí odkaz:
http://arxiv.org/abs/2408.05084
Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many approaches i
Externí odkaz:
http://arxiv.org/abs/2408.05081
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices, which negat
Externí odkaz:
http://arxiv.org/abs/2408.05005
Autor:
Blank, Luise
In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundaries. While we concentrate on a given end-time target function the results hold also when the target function is given ov
Externí odkaz:
http://arxiv.org/abs/2408.04954
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub
Externí odkaz:
http://arxiv.org/abs/2408.04846
This paper introduces a novel approach to addressing uncertainty and associated risks in power system management, focusing on the discrepancies between forecasted and actual values of load demand and renewable power generation. By employing Economic
Externí odkaz:
http://arxiv.org/abs/2408.04830