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Carl Lundholm

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#machine learning Open access Sep 2026

Learning Nonlinear Finite Element Solution Operators Using Multilayer Perceptrons and Energy Minimization

Abstract. 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 discretization and aims at representing the solution operator by a multilayer perceptron that takes problem data variables as inpu...

Mats G. Larson, Carl Lundholm, Anna Sofie Persson · 1 citation

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