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The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a frameworkmore »to analyze dynamical processes on interconnected complex systems with directionality.

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Abstract Understanding the physical drivers of seasonal hydroclimatic variability and improving predictive skill remains a challenge with important socioeconomic and environmental implications for many regions around the world. Physics-based deterministic models show limited ability to predict precipitation as the lead time increases, due to imperfect representation of physical processes and incomplete knowledge of initial conditions. Similarly, statistical methods drawing upon established climate teleconnections have low prediction skill due to the complex nature of the climate system. Recently, promising data-driven approaches have been proposed, but they often suffer from overparameterization and overfitting due to the short observational record, and they often do not account for spatiotemporal dependencies among covariates (i.e., predictors such as sea surface temperatures). This study addresses these challenges via a predictive model based on a graph-guided regularizer that simultaneously promotes similarity of predictive weights for highly correlated covariates and enforces sparsity in the covariate domain. This approach both decreases the effective dimensionality of the problem and identifies the most predictive features without specifying them a priori. We use large ensemble simulations from a climate model to construct this regularizer, reducing the structural uncertainty in the estimation. We apply the learned model to predict winter precipitation in the southwesternmore »United States using sea surface temperatures over the entire Pacific basin, and demonstrate its superiority compared to other regularization approaches and statistical models informed by known teleconnections. Our results highlight the potential to combine optimally the space–time structure of predictor variables learned from climate models with new graph-based regularizers to improve seasonal prediction.« less