{"ID":2878565,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.17995","arxiv_id":"2508.17995","title":"Topology Aware Neural Interpolation of Scalar Fields","abstract":"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.","short_abstract":"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 d...","url_abs":"https://arxiv.org/abs/2508.17995","url_pdf":"https://arxiv.org/pdf/2508.17995v2","authors":"[\"Mohamed Kissi\",\"Keanu Sisouk\",\"Joshua A. Levine\",\"Julien Tierny\"]","published":"2025-08-25T13:04:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\",\"cs.GR\"]","methods":"[]","has_code":false,"code_links":[{"ID":610493,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2878565,"paper_url":"https://arxiv.org/abs/2508.17995","paper_title":"Topology Aware Neural Interpolation of Scalar Fields","repo_url":"https://github.com/MohamedKISSI/Topology-Aware-Neural-Interpolation-of-Scalar-Fields.git","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}