2 papers
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…
math.NA2025
Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators
Erik Burman, Mats G. Larson, Karl Larsson +1
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct b…