82 citations · 134 across the 16 of their papers we have counts for
5 papers · 1 filter
Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation
Yuankai Teng, Zhu Wang, Lili Ju +2
Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks.…
On p-Willmore Disks with Boundary Energies
Anthony Gruber, Álvaro Pámpano, Magdalena Toda
We consider an energy functional on surface immersions which includes contributions from both boundary and interior. Inspired by physical examples, the boundary is modeled as the c…
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
Anthony Gruber, Max Gunzburger, Lili Ju +1
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite t…
Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique
Anthony Gruber
We prove that immersions of planar domains are uniquely specified by their Jacobian determinant, curl function, and boundary values. This settles the two-dimensional version of an…
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
Anthony Gruber, Max Gunzburger, Lili Ju +2
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Lev…