Data-driven linear analysis from partial measurements

Develop a general method for data-driven linear analysis of partially observed dynamical systems that produces meaningful insight into the linear dynamics within a subdomain despite coupling to unmeasured external state variables.

Background

The paper studies data-driven linear analysis when measurements are available only on a spatial subdomain and possibly an adjacent boundary region, while the remaining state variables outside the measurement area are unobserved. The authors partition the linear operator into subdomain, boundary, and exterior blocks and show that the subdomain resolvent depends not only on the internally identifiable operators but also on feedback pathways through the unmeasured exterior dynamics.

Although NSDMDc can estimate the coupling from the subdomain and boundary states for advection-dominated systems, this is insufficient in the general case because disturbances within the subdomain can drive unmeasured exterior states that subsequently feed back into the subdomain. The paper therefore identifies the development of a general partial-measurement method as an unresolved challenge, beyond the special upstream-boundary setting treated by NSDMDc.