Notation

Notation used throughout the wiki.

Symbol	Meaning
$\Omega \subset {\mathbb{R}}^n$	bounded Lipschitz domain (body)
$\Gamma =\partial \Omega$, $\nu$	boundary, outward unit normal
$\gamma$	true conductivity
$\sigma$	conductivity estimate / optimisation variable
$u$	electric potential (voltage) in $\Omega$
$\mathbf{J}=-\gamma \nabla u$	current density
$f=u{|}_{\partial \Omega }$	boundary voltage (Dirichlet data)
$g=\gamma {\partial }_{\nu }u{|}_{\partial \Omega }$	boundary current density (Neumann data)
${\Lambda }_{\gamma }$	Dirichlet-to-Neumann Map $f\mapsto g$
${\Lambda }_{\gamma }^{-1}={\mathcal{R}}_{\gamma }$	Neumann-to-Dirichlet Map $g\mapsto f$
${\phi }_i$	finite element basis functions
$M_{ij}=\int {\phi }_i{\phi }_j$	Mass Matrix
$K_{ij}=\int \nabla {\phi }_i\cdot \nabla {\phi }_j$	Stiffness Matrix
$L_{\gamma }$, $(L_{\gamma }{)}_{ij}=\int \gamma \nabla {\phi }_i\cdot \nabla {\phi }_j$	Weighted Stiffness Matrix
$M_{\Gamma }$, $K_{\Gamma }$	Boundary Mass and Stiffness Matrices
$\lambda$	adjoint state (Lagrange multiplier)
$J(\sigma )$	data misfit functional
$\mathcal{R}(\sigma )$, $\beta$	regulariser, regularisation parameter
$d(\cdot ,\cdot )$	data distance / metric
$J$ (matrix), $r$	Jacobian and residual in [[Gauss-Newton Method
$L_{\text{LM}}$	[[Levenberg-Marquardt Method
$\beta (t)$, $\bar{\alpha }(t)$	diffusion Noise Schedule and cumulative signal factor
${\epsilon }_{\theta }(x,t)$	noise-prediction network
$s_{\theta }(x,t)$	learned Score Function

Note the double use of $\beta$ (regularisation parameter vs. noise schedule) and of $J$ (misfit vs. Jacobian). The meaning is always clear from the context of the article.