4 papers
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…
Optimal Control of Thin-Film Flow on a Flexible Topography
S. Alrashidy, A. Kalogirou, D. Kalise +1
This work presents a mathematical model for the optimal control of thin-film flows over a flexible substrate influenced by an external force. The objective is to find the optimal d…
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 bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness
Anne Boschman, Luis Espath, Kris van der Zee
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end…