Deposition of liquid metal, layer by layer or melt bead by melt bead, is a process that is well suited for the rapid fabrication, without tooling, of metal parts having complex geometries and functionally graded microstructure. It follows that a parametric model representation of such a process is important for purposes of process control and optimization. Layer-by-layer liquid-metal deposition represents a special case of the general process of unsteady-state heat deposition.  Accordingly, this process is characterized by a high level of insensitivity of the time-dependent temperature field within the metal structure being formed to certain details of the energy source or melt deposit per instance. This insensitivity provides the basis for the application of a general algorithmic structure for inverse modeling of layer-by-layer liquid-metal deposition. In turn, the formalism of inverse modeling establishes a mathematical framework for the construction of a parametric model representation of layer-by-layer deposition processes in general.