3 papers
math.NA2026
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…
math.NA2025
An -adaptive finite element method using neural networks for parametric self-adjoint elliptic problem
Danilo Aballay, Federico Fuentes, Vicente Iligaray +5
This work proposes an -adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting i…
math.NA2024
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…