4 papers
Latent Inversion of Material Coefficients from Boundary Data via Finite Tests and Neural Surrogates
Erik Burman, Mats G. Larson, Karl Larsson +1
We reconstruct a spatially varying material coefficient in a scalar elliptic equation from finitely many boundary excitations, each producing a full Dirichlet trace. To mitigate th…
Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
Erik Burman, Mats G. Larson, Karl Larsson +1
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. Th…
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…
The Geometric Structure of Fully-Connected ReLU Layers
Jonatan Vallin, Karl Larsson, Mats G. Larson
We formalize and interpret the geometric structure of -dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of t…