# Topological Data Analysis for High-Dimensional Dynamic Process Monitoring

arXiv: https://arxiv.org/abs/2606.20443 · HTML: https://mlsanity.com/paper/2606.20443/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Deep Efficient Continuous Manifold Learning for Time Series Modeling](https://mlsanity.com/paper/2112.03379/) (2021)
- [Physics-Constrained Machine Learning for Chemical Engineering](https://mlsanity.com/paper/2508.20649/) (2025)
- [A Fast and Scalable Computational Topology Framework for the Euler Characteristic](https://mlsanity.com/paper/2311.11740/) (2023)
- [Convolutional Neural Nets in Chemical Engineering: Foundations, Computations, and Applications](https://mlsanity.com/paper/2101.04869/) (2021)
- [Topological Data Analysis for Multivariate Time Series Data](https://mlsanity.com/paper/2204.13799/) (2022)
- [Convolutional Neural Networks: Basic Concepts and Applications in Manufacturing](https://mlsanity.com/paper/2210.07848/) (2022)
- [PERCEPT: a new online change-point detection method using topological data analysis](https://mlsanity.com/paper/2203.04246/) (2022)
- [A Digital Twin Simulator of a Pastillation Process with Applications to Automatic Control based on Computer Vision](https://mlsanity.com/paper/2503.16539/) (2025)

## Abstract (arXiv)

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.