Singular equivalence and singular locus

For a commutative Gorenstein Noetherian ring R, we construct an affine scheme X solely from singularity category Dsg(R) of R such that there is a finite surjective morphism X → Spec(R /I), where Spec(R /I) is the singular locus in Spec(R). As an application, for two such rings with equivalent singularity categories, we prove that the singular loci in their affine schemes have the same dimension.