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We construct two graphs: an undirected graph $\\mathcal{G}^u$ capturing spatial correlations across geography, and a directed graph $\\mathcal{G}^d$ capturing sequential relationships over time. We predict future samples of signal $\\mathbf{x}$, assuming it is \"smooth\" with respect to both $\\mathcal{G}^u$ and $\\mathcal{G}^d$, where we design new $\\ell_2$ and $\\ell_1$-norm variational terms to quantify and promote signal smoothness (low-frequency reconstruction) on a directed graph. We design an iterative algorithm based on alternating direction method of multipliers (ADMM), and unroll it into a feed-forward network for data-driven parameter learning. 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