I'm a bit confused about when to use RMSE, R2 or Pearsons Correlation Coefficient (Rp). I've read some papers that reported RMSE and Rp and didn't even mention R2, but I also found papers reporting only R2. My doubt is in which kind of problems should I use each of these metrics. By reading these papers I noticed the authors were more concerned about the magnitude of errors and used RMSE and Rp to evaluate the performance.
On the other hand, the papers reporting R2 were more interested in comparing different models to solve a specific problem, for example Xu et al compared the performance of single- and multi-task neural network to predict the binding affinity of molecules on different protein targets using R2 values (https://www.ncbi.nlm.nih.gov/pubmed/28872869).