Sensor placement via large deviations in the eikonal equation

Ftouhi I, Zuazua Iriondo E (2025)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Open Access Link: https://arxiv.org/abs/2508.21469

Abstract

In this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domain. To tackle this natural geometric performance criterion, formulated in terms of distance functions, we combine tools from geometric analysis with a classical result of Varadhan [21], which provides an efficient approximation of the distance function via the solution of a simple elliptic PDE. The effectiveness of the proposed approach is demonstrated through illustrative numerical simulations.

Authors with CRIS profile

Ilias Ftouhi Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Ftouhi, I., & Zuazua Iriondo, E. (2025). Sensor placement via large deviations in the eikonal equation. (Unpublished, Submitted).

MLA:

Ftouhi, Ilias, and Enrique Zuazua Iriondo. Sensor placement via large deviations in the eikonal equation. Unpublished, Submitted. 2025.

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