7 papers
The Push-Forward Transform for Continuous and Robust Comparison of Dynamic Shapes
Roua Rouatbi, Juan-Esteban Suarez Cardona, Ivo F. Sbalzarini
We introduce a mathematical framework for shape comparison based on mapping functions from the shape domain to a common reference domain. This Push-Forward Transform enables invari…
A Variational Framework for the Complexity of PDE Solutions
Juan Esteban Suarez Cardona, Holger Boche, Gitta Kutyniok
Partial Differential Equations (PDEs) are fundamental mathematical models for describing physical phenomena, yet most PDEs of practical interest require numerical approximations. T…
A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes
Roua Rouatbi, Juan-Esteban Suarez Cardona, Alba Villaronga-Luque +2
We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological propertie…
Hybrid Surrogate Models: Circumventing Gibbs Phenomenon for Partial Differential Equations with Finite Shock-Type Discontinuities
Juan-Esteban Suarez Cardona, Shashank Reddy, Michael Hecht
We introduce the concept of Hybrid Surrogate Models (HSMs) -- combining multivariate polynomials with Heavyside functions -- as approximates of functions with finitely many jump di…
Ensuring Topological Data-Structure Preservation under Autoencoder Compression due to Latent Space Regularization in Gauss--Legendre nodes
Chethan Krishnamurthy Ramanaik, Juan-Esteban Suarez Cardona, Anna Willmann +3
We formulate a data independent latent space regularisation constraint for general unsupervised autoencoders. The regularisation rests on sampling the autoencoder Jacobian in Legen…
Learning Partial Differential Equations by Spectral Approximates of General Sobolev Spaces
Juan-Esteban Suarez Cardona, Phil-Alexander Hofmann, Michael Hecht
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we real…