9 papers · 1 filter
Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization
ElÃas 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…
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…