1. A method for determining mappings between high-dimensional measured samples and a reduced-dimensional manifold, comprising: acquiring samples of a physical system, the samples having a high number of dimensions; determining a low number of dimensions of a manifold embedded in a space of the high-dimensional samples; fitting local charts having the dimensions of the low number of dimensions of the manifold to selected high-dimensional samples; and connecting the charts to determine a forward mapping from any high-dimensional sample to a coordinate on the manifold and a reverse mapping from any coordinate on the manifold to a corresponding point in high-dimensional sample space.