13 citations · 14 across the 10 of their papers we have counts for
11 papers
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 Green-Integral-Constrained Neural Solver with Stochastic Physics-Informed Regularization
Mohammad Mahdi Abedi, David Pardo, Tariq Alkhalifah
Standard physics-informed neural networks (PINNs) struggle to simulate highly oscillatory Helmholtz solutions in heterogeneous media because pointwise minimization of second-order…
Robust Deep FOSLS for Transmission Problems
Alejandro Duque, Paulina Sepúlveda, Carlos Uriarte +2
This work presents a robust, energy-based deep learning framework for solving transmission problems in heterogeneous media, including cases with discontinuous material scenarios. W…
RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
Pablo Herrera, Jamie M. Taylor, Carlos Uriarte +3
Solving Partial Differential Equations (PDEs) using neural networks presents different challenges, including integration errors and spectral bias, often leading to poor approximati…
A Least-Squares-Based Regularity-Conforming Neural Networks (LS-ReCoNNs) for Solving Parametric Transmission Problems
Shima Baharlouei, Jamie Taylor, David Pardo
This article focuses on solving parametric transmission problems in one and two spatial dimensions. These problems belong to a class of partial differential equations that arise in…
Efficient Numerical Integration for Finite Element Trunk Spaces in 2D and 3D using Machine Learning: A new Optimisation Paradigm to Construct Application-Specific Quadrature Rules
Tomas Teijeiro, Pouria Behnoudfar, Jamie M. Taylor +2
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforwar…
Stochastic Quadrature Rules for Solving PDEs using Neural Networks
Jamie M. Taylor, David Pardo
We examine the challenges associated with numerical integration when applying Neural Networks to solve Partial Differential Equations (PDEs). We specifically investigate the Deep R…
A Least-Squares-Based Neural Network (LS-Net) for Solving Linear Parametric PDEs
Shima Baharlouei, Jamie M. Taylor, Carlos Uriarte +1
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Net…
Optimizing Variational Physics-Informed Neural Networks Using Least Squares
Carlos Uriarte, Manuela Bastidas, David Pardo +2
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for t…
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…
Adaptive Deep Fourier Residual method via overlapping domain decomposition
Jamie M. Taylor, Manuela Bastidas, Victor M. Calo +1
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 di…