  We give a means for measuring the equation of evolution of a complex scalar
field that is known to obey an otherwise unspecified (2+1)-dimensional
dissipative nonlinear parabolic differential equation, given field moduli over
three closely-spaced planes. The formalism is tested by recovering nonlinear
interactions and the associated equation of motion from simulated data for a
range of (2+1)-dimensional nonlinear systems, including those which exhibit
spontaneous symmetry breaking. The technique is of broad applicability, being
able to infer a wide class of partial differential equations, which govern
systems ranging from nonlinear optics to quantum fluids.
