35 citations · 116 across the 19 of their papers we have counts for
3 papers · 1 filter
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…