# Neural Persistence Dynamics

arXiv: https://arxiv.org/abs/2405.15732 · HTML: https://mlsanity.com/paper/2405.15732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 63 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence](https://mlsanity.com/paper/2006.07882/) (2020)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Fully probabilistic deep models for forward and inverse problems in parametric PDEs](https://mlsanity.com/paper/2208.04856/) (2022)
- [Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems](https://mlsanity.com/paper/2402.11722/) (2024)
- [Subsampling Methods for Persistent Homology](https://mlsanity.com/paper/1406.1901/) (2014)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://mlsanity.com/paper/2306.03801/) (2023)
- [Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology](https://mlsanity.com/paper/1707.06683/) (2017)
- [Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems](https://mlsanity.com/paper/2009.08972/) (2020)
- [Capturing Dynamics of Time-Varying Data via Topology](https://mlsanity.com/paper/2010.05780/) (2020)
- [Extracting Persistent Clusters in Dynamic Data via M"obius inversion](https://mlsanity.com/paper/1712.04064/) (2017)
- [Spatio-temporal Persistent Homology for Dynamic Metric Spaces](https://mlsanity.com/paper/1812.00949/) (2018)

## Abstract (arXiv)

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In such systems, patterns emerge from (local) interactions among self-propelled entities. While several well-understood governing equations for motion and interaction exist, they are notoriously difficult to fit to data, as most prior work requires knowledge about individual motion trajectories, i.e., a requirement that is challenging to satisfy with an increasing number of entities. To evade such confounding factors, we investigate collective behavior from a textittopological perspective, but instead of summarizing entire observation sequences (as done previously), we propose learning a latent dynamical model from topological features textitper time point. The latter is then used to formulate a downstream regression task to predict the parametrization of some a priori specified governing equation. We implement this idea based on a latent ODE learned from vectorized (static) persistence diagrams and show that a combination of recent stability results for persistent homology justifies this modeling choice. Various (ablation) experiments not only demonstrate the relevance of each model component but provide compelling empirical evidence that our proposed model - textitNeural Persistence Dynamics - substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.