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The Department of Mechanical, Materials, and Aerospace Engineering presents its spring 2025 seminar series featuring Ankit Srivastava, professor of mechanical engineering at Illinois Tech, who will present “Operator Theoretic Measure of Causality in Linear Dynamical Systems,” which is a collaborative work with Professors Scott Dawson, and Lou Cattafesta. This seminar is open to the public and will take place on Wednesday, April 23, from 12:45–1:45 p.m. in room 104 of the Rettaliata Engineering Center.

Abstract

We present a novel operator-theoretic framework for analyzing causality in linear dynamical systems, with applications to fluid mechanics. Our approach shows that the matrix exponential encodes causal relationships between system modes, providing a physics-based alternative to statistical measures such as Granger causality and Transfer Entropy. Instead of inferring causality from time-series data, our Linear Operator Causality Analysis (LOCA) leverages linearized governing equations to yield more rigorous measures of causal interactions in deterministic systems. We establish connections between our framework and key system properties including controllability, observability, and transient growth. We also introduce a data-driven methodology that estimates causal connections directly from time series data. Applied to linearized channel flow, our approach successfully captures both direct and indirect causal interactions among flow structures while mitigating common issues in data-driven causality analyses. This framework provides new insights into modal interactions and perturbation propagation in fluid flows and other dynamical systems.

For more about the speaker, Professor of Mechanical Engineering Ankit Srivastava, please visit his directory page on our website.