Inverse Analysis of Rapid and Localized Energy Deposition

This paper examines multiscale inverse analysis of rapid and localized energy deposition, where there exists extremely strong filtering of spatial and temporal structure within the associated diffusion pattern. This strong filtering tends to establish conditions where system identification, or in particular reconstruction of detailed features of the energy source, based on data-driven inverse analysis of the diffusion pattern alone is not well posed. An accurate and well-posed characterization of rapid energy deposition processes should be in terms of two distinctly separate scales for both spatial and temporal structures. Accordingly, the inverse rapid and localized energy deposition problem requires a formulation with respect to system identification and parameterization that should be cast in terms of two separate sets of parameters. One should represent energy source characteristics on spatial and temporal scales commensurate with that of thermal diffusivity within the material. The other parameter set should represent energy source characteristics on spatial and temporal scales commensurate with those of surface phenomena. The general procedure presented here for inverse analysis of rapid and localized energy deposition is formulated in terms of these two separate sets of parameters.