13 citations · 14 across the 8 of their papers we have counts for
4 papers · 1 filter
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…