Topological signatures for finance, climate, and fluid dynamics.
Topological data analysis is unusually well-suited to non-linear time series and dynamical systems. A sliding window in phase space carries the topology of an underlying attractor; that topology often changes sharply at the very moments—regime transitions, crashes, onsets, withdrawals—that domain scientists most want to detect, and that ordinary descriptors most often miss. The work in this project carries persistence diagrams, Euler characteristic surfaces, and complex-network constructions into climate science, statistical finance, and fluid mechanics.
What unites the three application domains is the topologist's working assumption: the data is high-dimensional, but the regime is not. Find the regime, find the change-point, find the descriptor that survives the noise. The papers below report on attempts at all three, in collaboration with NIT Sikkim, Montana Tech, Oxford climate, and several others.
Active threads
- Climate. Predicting the onset and withdrawal of the Indian monsoon from historical wind data; topological signatures of the polar vortex and Montana weather.
- Statistical finance. Identifying extreme events in the stock market; complex-network analysis of cryptocurrency crashes; causality of COVID-19-induced market crashes.
- Fluid mechanics. Topological characterization of churn flow and unsupervised correction to flow-regime maps in vertical pipes.
Collaborators
- Md. Nurujjaman, NIT Sikkim
- Atish Mitra, Montana Technological University
- Joshua Dorrington, Kristian Strommen, Maria Sánchez Muniz—climate
- Anish Rai, Buddha Nath Sharma, Salam Rabindrajit Luwang—finance
- Brady Koenig, Burt Todd—fluid mechanics
- Chittaranjan Hens, Kanish Debnath, Kundan Mukhia