In this talk, we introduce a new type of neural network called resolution invariant deep operator network (RDONet), which is an extension of the DeepONet, for the numerical approximation of partial differential equations (PDEs). Compared with DeepONet, our approach can handle inputs of different resolutions/discretizations without the re-tranning of network parameters. RDONet can also resolve PDEs with complex geometries where neural operator network failed. We demonstrate the efficiency of our method with numerical experiments.