Approximating a System Using an Abstract Geometrical Space

A computer-accessible memory medium that stores program instructions for approximating a system, wherein the program instructions are executable by a processor to:

• store a representation of a family of systems in a computer memory, wherein the representation of the family of systems comprises a plurality of parameters, and wherein the family of systems comprises models of corresponding real-world systems;
• determine an embedding of the family of systems into an abstract geometrical space with a metric, wherein the abstract geometrical space is continuous, wherein the abstract geometrical space is defined by the parameters, wherein at least some coordinates of the abstract geometrical space specify values for the parameters of systems of the family of systems, and wherein the abstract geometrical space comprises a grid of discrete points representing respective discrete approximations of systems of the family of systems;
• determine a first point in the abstract geometrical space corresponding to a desired instance of a system, wherein the coordinates of the first point specify values for the parameters of the desired instance of the system;
• sample the abstract geometrical space using a mapping of a well-distributed set of points from a Euclidean space of the parameters to the abstract geometrical space, wherein the mapping fairly maps the Euclidean space to the abstract geometrical space;
• determine a nearest discrete point to the first point in the abstract geometrical space in accordance with the metric based on said sampling, wherein the nearest discrete point specifies values for parameters for a substantially optimal discrete approximation of the desired instance of the system;
• and
• store the specified values for the discrete approximation, wherein the specified values of are useable to implement the discrete approximation of the desired instance of the system.