Complex　three-dimensional　(3D)　mesostructures　in　advanced　functional　materials　are　attracting　increasing　interest,　due　to　their　widespread　applications.　Mechanically-guided　3D　assembly　through　compressive　buckling　provides　deterministic　routes　to　a　rich　diversity　of　3D　mesostructures　and　microelectronic　devices,　with　feature　sizes　ranging　from　sub-microscale　to　millimeter-scale.　Existing　studies　established　inverse　design　methods　that　map　the　target　3D　geometry　onto　an　unknown　2D　precursor,　but　mainly　focusing　on　filamentary　ribbon-type　geometries.　Although　strategies　relying　on　spatial　thickness　variation　of　2D　precursors　have　been　reported　to　achieve　inverse　design　of　3D　surfaces,　this　could　lead　to　a　lack　of　compatibility　with　well-developed　planar　fabrication　technologies.　In　the　framework　of　buckling-guided　3D　assembly,　this　paper　presents　a　computational　method　based　on　topology　optimization　to　solve　the　inverse　design　problem　of　3D　surfaces　from　2D　precursors　with　uniform　thickness　distributions.　Specifically,　curvy　ribbon　components　were　exploited　to　discretize　nondevelopable　target　surfaces,　and　then　optimized　to　ensure　that　the　assembled　3D　surface　has　the　best　match　with　the　target　geometry.　Combined　computational　and　experimental　studies　over　a　dozen　of　elaborate　examples,　encompassing　both　the　caged　and　even　general　target　surfaces,　demonstrate　the　effectiveness　and　applicability　of　the　proposed　method.　©　2021　Elsevier　Ltd