# Topology Aware Neural Interpolation of Scalar Fields

arXiv: https://arxiv.org/abs/2508.17995 · HTML: https://mlsanity.com/paper/2508.17995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 51 of its 89 references that are in the map.
- First posted on arXiv 25 Aug 2025.

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Super SloMo: High Quality Estimation of Multiple Intermediate Frames for Video Interpolation](https://mlsanity.com/paper/1712.00080/) (2017)
- [Softmax Splatting for Video Frame Interpolation](https://mlsanity.com/paper/2003.05534/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Depth-Aware Video Frame Interpolation](https://mlsanity.com/paper/1904.00830/) (2019)
- [Video Frame Interpolation via Adaptive Separable Convolution](https://mlsanity.com/paper/1708.01692/) (2017)
- [Real-Time Intermediate Flow Estimation for Video Frame Interpolation](https://mlsanity.com/paper/2011.06294/) (2020)
- [FILM: Frame Interpolation for Large Motion](https://mlsanity.com/paper/2202.04901/) (2022)
- [AdaCoF: Adaptive Collaboration of Flows for Video Frame Interpolation](https://mlsanity.com/paper/1907.10244/) (2019)
- [Stochastic subgradient method converges on tame functions](https://mlsanity.com/paper/1804.07795/) (2018)
- [BMBC:Bilateral Motion Estimation with Bilateral Cost Volume for Video Interpolation](https://mlsanity.com/paper/2007.12622/) (2020)
- [Asymmetric Bilateral Motion Estimation for Video Frame Interpolation](https://mlsanity.com/paper/2108.06815/) (2021)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [FLAVR: Flow-Agnostic Video Representations for Fast Frame Interpolation](https://mlsanity.com/paper/2012.08512/) (2020)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [Enhanced Quadratic Video Interpolation](https://mlsanity.com/paper/2009.04642/) (2020)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport](https://mlsanity.com/paper/1805.08331/) (2018)

## Abstract (arXiv)

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.