9 papers
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…
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…