I will discuss some examples illustrating how manifold learning can lead to data-driven models of dynamical systems where the equations, the dependent variables, the parameters, and even the independent variables (space and time) "emerge" from observations of the system dynamics. I will focus, in particular, on transformations between different observations of the same model, heterogeneous data fusion, and the subject of "gauge invariant" data mining, i.e. data mining that is invariant to the measuring instrument. I will also show some links between the manifold learning implementation and the neural network implementation of tasks arising in the above context.
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