35 citations · 116 across the 19 of their papers we have counts for
19 papers
Stable time-stepping via residual minimization: finite-element and neural-network approximations for transient parabolic problems
Judit Muñoz-Matute, Sergio Rojas
We propose a time-stepping minimum-residual (MinRes) framework for transient coercive variational problems, applicable to finite-element and neural-network trial approximations. Fo…
Neural network approximation in discrete dual norms with adaptive test spaces
Tanakorn Udomworarat, Ignacio Brevis, Kristoffer G. van der Zee +1
In robust variational physics-informed neural networks (RVPINNs), the loss function is formulated in terms of the Riesz representative of the variational residual within a discrete…
A Residual Minimization approach for Nonlinear Partial Differential Equations set in Banach spaces
Ignacio Muga, Jorge Perera, Sergio Rojas +1
In this work, we propose and analyze a residual-minimization strategy for the numerical solution of nonlinear PDEs posed in Banach spaces. Given a finite-dimensional trial space an…
A posteriori analysis of neural network approximations
Thomas Führer, Sergio Rojas
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily g…
Neural network methods for Neumann series problems of Perron-Frobenius operators
T. Udomworarat, I. Brevis, M. Richter +2
Problems related to Perron-Frobenius operators (or transfer operators) have been extensively studied and applied across various fields. In this work, we propose neural network meth…
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…