13 citations · 14 across the 10 of their papers we have counts for
5 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 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…