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With the advent of increasingly elaborate experimental techniques in physics, chemistry and materials sciences, measured data are becoming bigger and more complex. The observables are typically a function of several stimuli resulting in multidimensional data sets spanning a range of experimental parameters. As an example, a common approach to study ferroelectric switching is to observe effects of applied electric field, but switching can also be enacted by pressure and is influenced by strain fields, material composition, temperature, time, etc. Moreover, the parameters are usually interdependent, so that their decoupling toward univariate measurements or analysis may not be straightforward. On the other hand, both explicit and hidden parameters provide an opportunity to gain deeper insight into the measured properties, provided there exists a well-defined path to capture and analyze such data. Here, we introduce a new, two-dimensional approach to represent hysteretic response of a material system to applied electric field. Utilizing ferroelectric polarization as a model hysteretic property, we demonstrate how explicit consideration of electromechanical response to two rather than one control voltages enables significantly more transparent and robust interpretation of observed hysteresis, such as differentiating between charge trapping and ferroelectricity. Furthermore, we demonstrate how the new data representation readily fits into a variety of machine-learning methodologies, from unsupervised classification of the origins of hysteretic response via linear clustering algorithms to neural-network-based inference of the sample temperature based on the specific morphology of hysteresis. 

Abstract Scanning Probe Microscopy (SPM) based techniques probe material properties over microscale regions with nanoscale resolution, ultimately resulting in investigation of mesoscale functionalities. Among SPM techniques, piezoresponse force microscopy (PFM) is a highly effective tool in exploring polarization switching in ferroelectric materials. However, its signal is also sensitive to sample‐dependent electrostatic and chemo‐electromechanical changes. Literature reports have often concentrated on the evaluation of theOff‐fieldpiezoresponse, compared toOn‐fieldpiezoresponse, based on the latter's increased sensitivity to non‐ferroelectric contributions. Using machine learning approaches incorporatingboth Off‐andOn‐fieldpiezoresponse response as well asOff‐fieldresonance frequency to maximize information, switching piezoresponse in a defect‐rich Pb(Zr,Ti)O₃thin film is investigated. As expected, one major contributor to the piezoresponse is mostly ferroelectric, coupled with electrostatic phenomena duringOn‐fieldmeasurements. A second component is electrostatic in nature, while a third component is likely due to a superposition of multiple non‐ferroelectric processes. The proposed approach will enable deeper understanding of switching phenomena in weakly ferroelectric samples and materials with large chemo‐electromechanical response.