3 papers
math.NA2026
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…
math.NA2025
Inexact Uzawa-Double Deep Ritz Method for Weak Adversarial Neural Networks
Emin Benny-Chacko, Ignacio Brevis, Luis Espath +1
Residual minimization in dual norms is central to Weak Adversarial Neural Network (WAN) approaches for solving partial differential equations (PDEs). This framework naturally leads…
math.NA2025
Neural Network Dual Norms for Minimal Residual Finite Element Methods
Hamd Alsobhi, Emin Benny-Chacko, Ignacio Brevis +1
Minimal-residual methods for PDEs with a residual in a dual space are non-trivial to guarantee stability. We present a minimal-residual finite element method in which the solution…