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Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

 

Machine learning influences numerous aspects of modern society, empowers new technologies, from Alphago to ChatGPT, and increasingly materializes in consumer products such as smartphones and self-driving cars. Despite the vital role and broad applications of artificial neural networks, we lack systematic approaches, such as network science, to understand their underlying mechanism. The difficulty is rooted in many possible model configurations, each with different hyper-parameters and weighted architectures determined by noisy data. We bridge the gap by developing a mathematical framework that maps the neural network’s performance to the network characters of the line graph governed by the edge dynamics of stochastic gradient descent differential equations. This framework enables us to derive a neural capacitance metric to universally capture a model’s generalization capability on a downstream task and predict model performance using only early training results. The numerical results on 17 pre-trained ImageNet models across five benchmark datasets and one NAS benchmark indicate that our neural capacitance metric is a powerful indicator for model selection based only on early training results and is more efficient than state-of-the-art methods.

 

Predicting the large-scale behaviour of complex systems is challenging because of their underlying nonlinear dynamics. Theoretical evidence now verifies that many complex systems can be simplified and still provide an insightful description of the phenomena of interest. 

We present efficient algorithms to learn the pa- rameters governing the dynamics of networked agents, given equilibrium steady state data. A key feature of our methods is the ability to learn without seeing the dynamics, using only the steady states. A key to the efficiency of our approach is the use of mean-field approximations to tune the parameters within a nonlinear least squares (NLS) framework. Our results on real networks demonstrate the accuracy of our approach in two ways. Using the learned parameters, we can: (i) Recover more accurate estimates of the true steady states when the observed steady states are noisy. (ii) Predict evolution to new equilibrium steady states after perturbations to the network topology. 

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network’s indirect connectivity. This realization leads to the emergence of an alternative theory called “concurrence percolation”, which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

 

Abstract The rapid rollout of the COVID-19 vaccine raises the question of whether and when the ongoing pandemic could be eliminated with vaccination and non-pharmaceutical interventions (NPIs). Despite advances in the impact of NPIs and the conceptual belief that NPIs and vaccination control COVID-19 infections, we lack evidence to employ control theory in real-world social human dynamics in the context of disease spreading. We bridge the gap by developing a new analytical framework that treats COVID-19 as a feedback control system with the NPIs and vaccination as the controllers and a computational model that maps human social behaviors into input signals. This approach enables us to effectively predict the epidemic spreading in 381 Metropolitan statistical areas (MSAs) in the US by learning our model parameters utilizing the time series NPIs (i.e., the stay-at-home order, face-mask wearing, and testing) data. This model allows us to optimally identify three NPIs to predict infections accurately in 381 MSAs and avoid over-fitting. Our numerical results demonstrate our approach’s excellent predictive power with R 2  > 0.9 for all the MSAs regardless of their sizes, locations, and demographic status. Our methodology allows us to estimate the needed vaccine coverage and NPIs for achieving R e to a manageable level and how the variants of concern diminish the likelihood for disease elimination at each location. Our analytical results provide insights into the debates surrounding the elimination of COVID-19. NPIs, if tailored to the MSAs, can drive the pandemic to an easily containable level and suppress future recurrences of epidemic cycles.