Methods and apparatus are provided for non-linear modeling of a physical system using two-dimensional look-up tables with bilinear interpolation. A non-linear function is evaluated for a complex input value by obtaining a two-dimensional (2D) look-up table with bilinear interpolation that represents the non-linear function; obtaining four points from the 2D look-up table that are in a vicinity of the complex input value; and generating a complex output value comprised of a bilinear combination of the four points. The non-linear function characterizes, for example, a power amplifier or an inverse of a power amplifier and the 2D look-up tables can be used, for example, to implement digital pre-distortion. The 2D look-up tables with bilinear interpolation can be used in a processor instruction as part of an instruction set of one or more of a scalar processor and a vector processor.