Empirical Nonlinear Dynamics:  Reconstructing the Dynamics of Real-World Systems from Available Data

This seminar presents an empirical dynamics approach that permits available data to ‘speak first’ regarding the nature of real-world processes generating them, and thus provides valuable guidance for subsequent modeling.  This data-driven approach is compatible with the classic scientific method in which “[scientists] are presented with observations and asked to build theories…to go backward, to solve for [the system] that made them” (Ellenberg, J. (2015), How Not to Be Wrong:  The Power of Mathematical Thinking, Penguin Books).  The discipline of nonlinear dynamics has mathematically solved the backward problem of reconstructing system dynamics from observed output when system equations are unknown. Nonlinear Time Series Analysis (NLTS) applies these results to empirically reconstruct system dynamics from observed time series records given that the true nature of real-world dynamic systems are largely unknown.  We can use reconstructed dynamics to distinguish whether observed volatility in records is most likely generated exogenously by random shocks to stable (self-correcting) systems, or endogenously by deterministic nonlinear behavior of unstable (non-self-correcting) systems.  We can further detect whether reconstructed deterministic dynamics are dissipative(meaning that the long-term evolution of system dynamics is bounded within a subset of phase space)—a valuable dimension-reducing property in modeling.  If so, long-term system dynamics can be modeled with relatively few degrees of freedom—regardless of the complexity or dimensionality of the original system.  Finally, we can use reconstructed low-dimensional dynamics to rigorously map out, and measure the impact of, conjectured system drivers.  The seminar will focus on several examples of research applying the NLTS approach to real-world economic and environmental problems.