🤖 AI Summary
This study addresses the challenge of monitoring dynamic processes in high-dimensional time series by proposing a novel approach that integrates topological data analysis (TDA) with neural ordinary differential equations (Neural ODEs). The method represents multivariate time series as manifolds, employs topological descriptors to capture their structural properties, and leverages Neural ODEs to model the continuous evolution of the system’s topology, enabling trajectory-based real-time event detection. To the best of our knowledge, this work is the first to combine TDA with Neural ODEs for process monitoring, overcoming limitations of conventional reconstruction- or Koopman-based methods in capturing topological changes in high-dimensional dynamics. Experimental results on industrial datasets demonstrate that the proposed method significantly outperforms baseline approaches—including PCA, autoencoders, and Koopman autoencoders—across multiple event detection tasks.
📝 Abstract
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.