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This paper presents a novel data-driven approach to identify partialdifferential equation (PDE) parameters of a dynamical system. Specifically, weadopt a mathematical "transport" model for the solution of the dynamical systemat specific spatial locations that allows us to accurately estimate the modelparameters, including those associated with structural damage. This isaccomplished by means of a newly-developed mathematical transform, the signedcumulative distribution transform (SCDT), which is shown to convert the generalnonlinear parameter estimation problem into a simple linear regression. Thisapproach has the additional practical advantage of requiring no a prioriknowledge of the source of the excitation (or, alternatively, the initialconditions). By using training data, we devise a coarse regression procedure torecover different PDE parameters from the PDE solution measured at a singlelocation. Numerical experiments show that the proposed regression procedure iscapable of detecting and estimating PDE parameters with superior accuracycompared to a number of recently developed machine learning methods.Furthermore, a damage identification experiment conducted on a publiclyavailable dataset provides strong evidence of the proposed method'seffectiveness in structural health monitoring (SHM) applications. The Pythonimplementation of the proposed system identification technique is integrated asa part of the software package PyTransKit(https://github.com/rohdelab/PyTransKit).

Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform