12 citations · 19 across the 8 of their papers we have counts for
11 papers · 1 filter
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…
A Shape-Newton Method for Free-boundary Problems Subject to The Bernoulli Boundary Condition
Yiyun Fan, John Billingham, Kristoffer van der Zee
We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme…
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…
Linearisation of the Travel Time Functional in Porous Media Flows
Paul Houston, Connor J. Rourke, Kristoffer G. Van der Zee
The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in…