28 citations · 46 across the 8 of their papers we have counts for
9 papers
Binary Black Hole Puncture Initial Data with Physics-Informed Neural Networks
Thiago Assumpção, Ignacio Brevis, Irene Pitsiladi +2
We present Pinndorama, a physics-informed neural network (PINN) code for solving the Hamiltonian constraint in the puncture formalism. The networks are trained solely on the govern…
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…
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 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…
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…
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…
Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach
Ignacio Brevis, Ignacio Muga, David Pardo +2
The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficien…
Neural Control of Discrete Weak Formulations: Galerkin, Least-Squares and Minimal-Residual Methods with Quasi-Optimal Weights
Ignacio Brevis, Ignacio Muga, Kristoffer G. van der Zee
There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete we…
Data-Driven Finite Elements Methods: Machine Learning Acceleration of Goal-Oriented Computations
Ignacio Brevis, Ignacio Muga, Kristoffer G. van der Zee
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interes…