Zobrazeno 1 - 10
of 168
pro vyhledávání: '"Makridakis, Charalambos"'
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose the Deep Uz
Externí odkaz:
http://arxiv.org/abs/2411.08702
In this work, we present a numerical solver for optimal control problems constrained by linear and semi-linear second-order elliptic PDEs. The approach is based on recasting the problem and includes an extension of Uzawa's algorithm to build approxim
Externí odkaz:
http://arxiv.org/abs/2410.17359
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with more standar
Externí odkaz:
http://arxiv.org/abs/2409.08362
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous minimisation proble
Externí odkaz:
http://arxiv.org/abs/2308.12891
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering problems. The
Externí odkaz:
http://arxiv.org/abs/2308.05423
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the resulting a
Externí odkaz:
http://arxiv.org/abs/2306.13784
Autor:
Kalaitzidou, Chrysovalantou, Grekas, Georgios, Zilian, Andreas, Makridakis, Charalambos, Rosakis, Phoebus
Through modelling and simulations we show that material instabilities play a dominant role in the mechanical behavior of the fibrous collagen Extracellular Matrix (ECM), as observed when the ECM is deformed by contractile biological cells. We compare
Externí odkaz:
http://arxiv.org/abs/2212.01213
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori error esti
Externí odkaz:
http://arxiv.org/abs/2203.00340
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We consider a model of energy minimization arising in the study of the mechanical behavior caused by cell contraction within a fibrous biological medium. The macroscopic model is based on the theory of non rank-one convex nonlinear elasticity for pha
Externí odkaz:
http://arxiv.org/abs/1907.01382