learned local maps 1manifold reconstruction 1multiscale methods 1nonlinear elliptic PDEs 1partition of unity 1tangent-space test functions 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.NA2026
Tangent-Space Multiscale Manifold Methods for Nonlinear Elliptic Problems
Mats G. Larson, Anna Persson
The paper proposes a tangent‑space multiscale manifold method that reconstructs fine‑scale solutions of heterogeneous nonlinear elliptic problems from a coarse state using localize…
math.NA2026
Numerical vortex resolution for the Gross-Pitaevskii equation in the rapid rotation Thomas-Fermi scaling
Patrick Henning, Anna Persson, Christos Pilichos
In this paper we analyze finite element approximations of ground states of the Gross-Pitaevskii equation in the rapid rotation Thomas-Fermi scaling. In this regime, the healing len…
cs.LG2025
Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization
Mats G. Larson, Carl Lundholm, Anna Persson
We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element…