19 citations · 19 across the 5 of their papers we have counts for
10 papers · 1 filter
Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization
Elías Caru, David Pardo, Judit Muñoz-Matute
We propose an r-adaptive neural algorithm for Isogeometric Analysis (IGA) based on residual minimization. The boundary-value problem is solved using a standard conforming Galerkin…
A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides
Ankit Chakraborty, Judit Munoz-Matute, Leszek Demkowicz +1
In this article, we propose a modified nonlinear Schrödinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic…
Regularity-Conforming Neural Networks (ReCoNNs) for solving Partial Differential Equations
Jamie M. Taylor, David Pardo, Judit Muñoz-Matute
Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of su…
Augmenting MRI scan data with real-time predictions of glioblastoma brain tumor evolution using faster exponential time integrators
Magdalena Pabisz, Judit Muñoz-Matute, Maciej Paszyński
We present a MATLAB code for exponential integrators method simulating the glioblastoma tumor growth. It employs the Fisher-Kolmogorov diffusion-reaction tumor brain model with log…
Multistage DPG time-marching scheme for nonlinear problems
Judit Muñoz-Matute, Leszek Demkowicz
In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG met…
Robust Variational Physics-Informed Neural Networks
Sergio Rojas, Paweł Maczuga, Judit Muñoz-Matute +2
We introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov-Galer…