Euler Characteristic Methods

Cumulative topology for time-series classification and regime detection.

The Euler characteristic is the simplest topological invariant: an alternating sum of simplex counts that, computed across a filtration, encodes more structure than its modesty suggests. Recent work uses Euler characteristic profiles and surfaces as fast, interpretable descriptors for time-series classification, regime detection in dynamical systems, and unsupervised flow-regime identification.

Active threads:

• Interpretable Classification of Time Series Using Euler Characteristic Surfaces—a fully interpretable pipeline for time-series classification, with Atish Mitra and the NIT Sikkim group; under review at Nature Scientific Reports.
• Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile—a mixup-style ECP for regime change in chaotic systems, submitted to Chaos.
• Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map—ECS for two-phase flow classification in vertical pipes, submitted to International Journal of Multiphase Flow.

Collaborators

• Atish Mitra, Montana Technological University
• Md. Nurujjaman, NIT Sikkim
• Buddha Nath Sharma, Salam Rabindrajit Luwang—NIT Sikkim
• Brady Koenig, Abigail Stein, Burt Todd—Montana Tech
• Vishal Mandal, Santanu Nandi