Learning-based partial differential equations (PDEs), which combine fundamental differential invariants into a non-linear regressor, have been successfully applied to several computer vision tasks. In this paper, we present a robust hybrid method that uses learning-based PDEs for detecting texts from natural scene images. Our method consists of both top-down and bottom-up processing, which are loosely coupled. We first use learning-based PDEs to produce a text confidence map. Text region candidates are then detected from the map by local binarization and connected component clustering. In each text region candidate, character candidates are detected based on their color similarity and then grouped into text candidates by simple rules. Finally, we adopt a two-level classification scheme to remove the non-text candidates. Our method has a flexible structure, where the latter part can be replaced with any connected component based methods to further improve the detection accuracy. Experimental results on public benchmark databases, ICDAR and SVT, demonstrate the superiority and robustness of our hybrid approach.