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We report the development and implementation of a hypothesis learning based automated experiment, in which the microscope operating in the autonomous mode identifies the physical laws behind the material's response. Specifically, we explore the bias induced transformations that underpin the functionality of broad classes of devices and functional materials from batteries and memristors to ferroelectrics and antiferroelectrics. Optimization and design of these materials require probing the mechanisms of these transformations on the nanometer scale as a function of the broad range of control parameters such as applied potential and time, often leading to experimentally intractable scenarios. At the same time, often the behaviors of these systems are understood within potentially competing theoretical models, or hypotheses. Here, we develop a hypothesis list that covers the possible limiting scenarios for the domain growth, including thermodynamic, domain wall pinning, and screening limited. We further develop and experimentally implement the hypothesis driven automated experiment in Piezoresponse Force Microscopy, autonomously identifying the mechanisms of the bias induced domain switching. This approach can be applied for a broad range of physical and chemical experiments with relatively low dimensional control parameter space and for which the possible competing models of the system behavior that ideally cover the full range of physical eventualities are known or can be created. These include other scanning probe microscopy modalities such as force distance curve measurements and nanoindentation, as well as materials synthesis and optimization.