Topology Aware Neural Interpolation of Scalar Fields

Fuente: arXiv
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Main Authors: Kissi, Mohamed, Sisouk, Keanu, Levine, Joshua A., Tierny, Julien
Format: Preprint
Published: 2025
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author Kissi, Mohamed
Sisouk, Keanu
Levine, Joshua A.
Tierny, Julien
author_facet Kissi, Mohamed
Sisouk, Keanu
Levine, Joshua A.
Tierny, Julien
contents This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted as keyframes, our interpolation approach aims at "inverting" the non-keyframe diagrams to produce plausible estimations of the corresponding, missing data. For this, we rely on a neural architecture which learns the relation from a time value to the corresponding scalar field, based on the keyframe examples, and reliably extends this relation to the non-keyframe time steps. We show how augmenting this architecture with specific topological losses exploiting the input diagrams both improves the geometrical and topological reconstruction of the non-keyframe time steps. At query time, given an input time value for which an interpolation is desired, our approach instantaneously produces an output, via a single propagation of the time input through the network. Experiments interpolating 2D and 3D time-varying datasets show our approach superiority, both in terms of data and topological fitting, with regard to reference interpolation schemes. Our implementation is available at this GitHub link : https://github.com/MohamedKISSI/Topology-Aware-Neural-Interpolation-of-Scalar-Fields.git.
format Preprint
id arxiv_https___arxiv_org_abs_2508_17995
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Topology Aware Neural Interpolation of Scalar Fields
Kissi, Mohamed
Sisouk, Keanu
Levine, Joshua A.
Tierny, Julien
Machine Learning
Computer Vision and Pattern Recognition
Graphics
This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted as keyframes, our interpolation approach aims at "inverting" the non-keyframe diagrams to produce plausible estimations of the corresponding, missing data. For this, we rely on a neural architecture which learns the relation from a time value to the corresponding scalar field, based on the keyframe examples, and reliably extends this relation to the non-keyframe time steps. We show how augmenting this architecture with specific topological losses exploiting the input diagrams both improves the geometrical and topological reconstruction of the non-keyframe time steps. At query time, given an input time value for which an interpolation is desired, our approach instantaneously produces an output, via a single propagation of the time input through the network. Experiments interpolating 2D and 3D time-varying datasets show our approach superiority, both in terms of data and topological fitting, with regard to reference interpolation schemes. Our implementation is available at this GitHub link : https://github.com/MohamedKISSI/Topology-Aware-Neural-Interpolation-of-Scalar-Fields.git.
title Topology Aware Neural Interpolation of Scalar Fields
topic Machine Learning
Computer Vision and Pattern Recognition
Graphics
url https://arxiv.org/abs/2508.17995