Transmission line matrix (TLM) is a discrete numerical time-domain mod
eling technique that can frequently be reduced to a closed-form soluti
on of the diffusion equation. In many cases the inverse operation of t
he TLM method is hampered by the imbalance between the number of avail
able equations and the number of unknowns. This article outlines the n
ature of the problem for Gaussian temperature profiles and shows how s
imple optimization can be used to obtain initial or early-time thermal
information.