We want to start a new project to solve a large-scale inverse problem (O(10^6) number of parameters) to invert for subsurface wave speeds. We will use FEM to solve forward and adjoint PDEs. In our project, we will need to have both sparse and dense solvers. Previously in similar projects, we were using PETSc library but today when I was searching for new libraries, SLATE library came to my attention (link). I was just wondering if there is any comparison between these two libraries from the performance point of view. Perhaps to make this question richer, I know Trilinos is another competitive library, but based on my personal experience and research that I did, I found PETSc is faster while Trilinos is more reliable. Please comment on this if you have any objections.