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math.NA2026
RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
Pablo Herrera, Jamie M. Taylor, Carlos Uriarte +3
Solving Partial Differential Equations (PDEs) using neural networks presents different challenges, including integration errors and spectral bias, often leading to poor approximati…
math.NA2026
A Residual Minimization approach for Nonlinear Partial Differential Equations set in Banach spaces
Ignacio Muga, Jorge Perera, Sergio Rojas +1
In this work, we propose and analyze a residual-minimization strategy for the numerical solution of nonlinear PDEs posed in Banach spaces. Given a finite-dimensional trial space an…