5 papers
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…
Source reconstruction algorithms for coupled parabolic systems from internal measurements of one scalar state
Cristhian Montoya, Ignacio Brevis, David Bolivar
This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where inte…
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…
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…
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…