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Representative volume element (RVE)-based analysis plays a central role in understanding the response of heterogeneous materials to properties and geometry of the constituents. However, the accuracy of RVE analysis on real-life materials requires extra effort on the identification of material constituents and characterization of imperfections (e.g., voids and cracks) introduced in the fabrication process. For these reasons, together with the multiscale and spatially varying nature of heterogeneities, analysis of heterogeneous materials can be prohibitively time-consuming. In this work, a fully convolutional network (FCN)-based framework called RVE-net is proposed to take advantage of the state-of-art use of FCNs in image segmentation and feedforward neural networks in universal approximation to accelerate multiscale analysis, identify microscale material properties, and automatically characterize defects in materials. In contrast with standard numerical methods (e.g., the finite element method), which depend heavily on domain discretization and local interpolations, the RVE-net takes microstructure images — parameterized by a coupled Heaviside and level-set field representation — and loading conditions as inputs. The aim is to directly learn the nonlinear interaction between the microstructures and their local responses in a hierarchical manner. This avoids burdensome discretization and interpolations, makes it possible to transfer the learned structure-response from one microstructure to another, and thus significantly accelerates the modeling of heterogeneous materials. Several numerical examples are performed to examine the performance of the proposed RVE-net. It is demonstrated that the RVE-net can leverage the power of graphics processing units (GPUs) in RVE analysis, inverse derivation of material constituents, and characterization of defects. • Fully convolutional neural network, RVE-net, developed for feature-driven analysis. • RVE-net takes microstructure images and loading conditions as inputs. • Method allows simultaneous parametric study on both geometry and load conditions. • RVE-net can discover both quantities and fields of interest from external data. • RVE-net enables knowledge transfer from existing to new instances. [ABSTRACT FROM AUTHOR]