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math.NA2024★ 4 cited
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…
cs.LG2024
Implicit Hypersurface Approximation Capacity in Deep ReLU Networks
Jonatan Vallin, Karl Larsson, Mats G. Larson
We develop a geometric approximation theory for deep feed-forward neural networks with ReLU activations. Given a -dimensional hypersurface in represented as t…