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We demonstrate that numerically computed approximations of Koopmaneigenfunctions and eigenvalues create a natural framework for data fusion inapplications governed by nonlinear evolution laws. This is possible because theeigenvalues of the Koopman operator are invariant to invertible transformationsof the system state, so that the values of the Koopman eigenfunctions serve asa set of intrinsic coordinates that can be used to map between differentobservations (e.g., measurements obtained through different sets of sensors) ofthe same fundamental behavior. The measurements we wish to merge can also benonlinear, but must be "rich enough" to allow (an effective approximation of)the state to be reconstructed from a single set of measurements. This approachrequires independently obtained sets of data that capture the evolution of theheterogeneous measurements and a single pair of "joint" measurements taken atone instance in time. Computational approximations of eigenfunctions and theircorresponding eigenvalues from data are accomplished using Extended DynamicMode Decomposition. We illustrate this approach on measurements ofspatio-temporal oscillations of the FitzHugh-Nagumo PDE, and show how to fusepoint measurements with principal component measurements, after which eitherset of measurements can be used to estimate the other set.

Data Fusion via Intrinsic Dynamic Variables: An Application of Data-Driven Koopman Spectral Analysis