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26 papers · 1 filter
Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs
Kateřina Škardová, Alexandre Daby-Seesaram, Martin Genet
We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Network…
Quasi-optimal interpolation of gradients and vector-fields on protected Delaunay meshes in
David M. Williams, Mathijs Wintraecken
There are very few mathematical results governing the interpolation of functions or their gradients on Delaunay meshes in more than two dimensions. Unfortunately, the standard tech…
A comparative analysis of metamodels for 0D cardiovascular models, and pipeline for sensitivity analysis, parameter estimation, and uncertainty quantification
John M. Hanna, Pavlos Varsos, Jérôme Kowalski +3
Zero-dimensional (0D) cardiovascular models are reduced-order models used to study global circulation dynamics and transport. They provide estimates of biomarkers (such as pressure…
Generalizing the SINDy approach with nested neural networks
Camilla Fiorini, Clément Flint, Louis Fostier +4
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinea…
Near-Field Linear Sampling Method forAxisymmetric Eddy Current Tomography
H. Haddar, M. K. Riahi
This paper is concerned with Eddy-Current (EC) nondestructive testing of conductive materials and focuses, in particular, on extending the well-known LinearSampling Method (LSM) to…
Rigid continuation paths II. Structured polynomial systems
Peter Bürgisser, Felipe Cucker, Pierre Lairez
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously u…