A heterostructured catalyst includes a 2-dimensional (2D) array of titanium including nanocavities that are all directly attached to a substrate. Each of the titanium including nanocavities have a pore with a nanopore size and a wall with a nanowall thickness. The titanium including nanocavities can be titania nanocavities with a metal layer or a metal compound layer on the titania nanocavities including inside the pores, or the titanium including nanocavities can include SrTiO3 or consist of SrTiO3, each with a surface layer of reduced SrTiO3.