Conveners
Free Boundary Problems in Data Science and Machine Learning: MS-13-1
- Eloi Martinet (JMU Würzburg)
Free Boundary Problems in Data Science and Machine Learning: MS-13-2
- Matthew Thorpe (University of Warwick)
Description
Organisers: Leon Bungert, Eloi Martinet, Thorpe Matthew
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Ryan Murray (North Carolina State University)07/09/2026, 14:00Free Boundary Problems in Data Science and Machine Learning
Recent work in machine learning has recognized that many standard algorithms for classification are strongly affected by adversarial attacks. Accordingly, a growing body of research has tried to identify ways to mitigate this issue. This talk will discuss a natural non-parametric formulation of this objective, which can be transformed into a standard classification problem that utilizes a...
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José A. Iglesias (University of Twente)07/09/2026, 14:30Free Boundary Problems in Data Science and Machine Learning
We focus on decomposability and extremality properties of nonlocal perimeters. Two archetypal types of these are the Gagliardo perimeter based on the eponymous seminorms and the nonlocal distributional Caccioppoli perimeter, both which can be considered with with finite and infinite interaction ranges.
A nonlocal notion of indecomposability associated to these perimeters is introduced, and...
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Adrien Weihs (University of California Los Angeles)07/09/2026, 15:00Free Boundary Problems in Data Science and Machine Learning
Operator learning constructs data-driven surrogates for maps between functions, but standard methods typically learn only a single operator. This talk introduces multiple-operator learning, where one model learns a family of related operators. I will present Multiple Neural Operators, together with approximation and generalization results showing that learning an operator family need not be...
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Yves van Gennip07/09/2026, 15:30Free Boundary Problems in Data Science and Machine Learning
Many machine-learning methods are related to gradient flows of cost functions. In this talk we present a method to establish many-data consistency of such methods via discrete-to-continuum limits. As examples we focus on total-variation and $p$-Laplacian flows. We also establish discrete Sobolev inequalities that elucidate the smoothing effect of regularisation terms in cost functions.
This...
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Riccardo Cristoferi08/09/2026, 10:30Free Boundary Problems in Data Science and Machine Learning
The analysis of Big Data is one of the most important challenges of the modern era. A first step in order to extract some information from a set of data is to partition it according to some notion of similarity. When only geometric features are used to define such a notion of similarity and no a priori knowledge of the data is available, we refer to it as the clustering problem.
Typically...
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Eloi Martinet (JMU Würzburg)08/09/2026, 11:00Free Boundary Problems in Data Science and Machine Learning
We propose a single-layer neural parametrization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks explicitly represent both the support and gauge functions of a convex body. We prove a universal approximation theorem for convex sets under this parametrization. Empirically, we demonstrate the method on shape optimization and inverse design tasks,...
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Simon Masnou (Université Lyon 1)08/09/2026, 11:30Free Boundary Problems in Data Science and Machine Learning
The talk will focus on neural operators with few parameters for approximating the Willmore flow of oriented or non-oriented interfaces in space dimensions 2 and 3.
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The proposed neural networks are trained on implicit representations of interfaces evolving by Willmore flow.
Various numerical simulations will be presented, together with applications to curve and surface reconstruction from... -
Samuel Weidemaier08/09/2026, 12:00Free Boundary Problems in Data Science and Machine Learning
We present a variational neural approach for computing global signed distance functions (SDFs) from unoriented point clouds, focusing on the medial axis as the unknown jump set of the SDF gradient. The method is based on the observation that the SDF gradient is smooth away from the medial axis, but jumps where the nearest-point projection onto the surface is not well-defined. We formulate SDF...
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