Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Taylor, Jamie M."'
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we improve the con
Externí odkaz:
http://arxiv.org/abs/2407.20417
Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor approximation
Externí odkaz:
http://arxiv.org/abs/2405.14110
The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural networks (VPINNs). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on approximatin
Externí odkaz:
http://arxiv.org/abs/2401.04663
Publikováno v:
Liq. Cryst., 51(6), 936-947, 2024
In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbors. By minimizing the free energy in the model and performing molecular dynamics, where, in both cases, the shape of the cell is a
Externí odkaz:
http://arxiv.org/abs/2312.00239
Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an appropriate
Externí odkaz:
http://arxiv.org/abs/2305.09578
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over uniform and
Externí odkaz:
http://arxiv.org/abs/2304.01802
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is the loss function to be minimised, which should ideally correspond to a norm of the error. In multiple problems, this error norm coincides with--or is
Externí odkaz:
http://arxiv.org/abs/2210.14129
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may arise in the
Externí odkaz:
http://arxiv.org/abs/2111.00217
We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques of Gamma convergence and demo
Externí odkaz:
http://arxiv.org/abs/2108.11133
Publikováno v:
J. Nonlinear Sci., 31, 87, 2021
Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across their enti
Externí odkaz:
http://arxiv.org/abs/2104.15029