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Over the last decade, there has been growing interest in learning the mapping from structural connectivity (SC) to functional connectivity (FC) of the brain. The spontaneous fluctuations of the brain activity during the resting-state as captured by functional MRI (rsfMRI) contain rich non-stationary dynamics over a relatively fixed structural connectome. Among the modeling approaches, graph diffusion-based methods with single and multiple diffusion kernels approximating static or dynamic functional connectivity have shown promise in predicting the FC given the SC. However, these methods are computationally expensive, not scalable, and fail to capture the complex dynamics underlying the whole process. Recently, deep learning methods such as GraphHeat networks and graph diffusion have been shown to handle complex relational structures while preserving global information. In this paper, we propose a novel attention-based fusion of multiple GraphHeat networks (A-GHN) for mapping SC-FC. A-GHN enables us to model multiple heat kernel diffusion over the brain graph for approximating the complex Reaction Diffusion phenomenon. We argue that the proposed deep learning method overcomes the scalability and computational inefficiency issues but can still learn the SC-FC mapping successfully. Training and testing were done using the rsfMRI data of 1058 participants from the human connectome project (HCP), and the results establish the viability of the proposed model. On HCP data, we achieve a high Pearson correlation of 0.788 (Desikan-Killiany atlas with 87 regions) and 0.773 (AAL atlas with 86 regions). Furthermore, experiments demonstrate that A-GHN outperforms the existing methods in learning the complex nature of the structure-function relation of the human brain. [ABSTRACT FROM AUTHOR]