DG singular equivalence and singular locus

For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X\to \mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}(R\mathrm{/}I)$, where $\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}(R\mathrm{/}I)$ is the singular locus in $\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}(R)$. As an application, for two such rings with equivalent DG singularity categories, we prove that the singular loci in their affine schemes have the same dimension.