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Gao TT, Barzel B, Yan G. Learning interpretable dynamics of stochastic complex systems from experimental data. Nat Commun 2024; 15:6029. [PMID: 39019850 PMCID: PMC11254936 DOI: 10.1038/s41467-024-50378-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 07/09/2024] [Indexed: 07/19/2024] Open
Abstract
Complex systems with many interacting nodes are inherently stochastic and best described by stochastic differential equations. Despite increasing observation data, inferring these equations from empirical data remains challenging. Here, we propose the Langevin graph network approach to learn the hidden stochastic differential equations of complex networked systems, outperforming five state-of-the-art methods. We apply our approach to two real systems: bird flock movement and tau pathology diffusion in brains. The inferred equation for bird flocks closely resembles the second-order Vicsek model, providing unprecedented evidence that the Vicsek model captures genuine flocking dynamics. Moreover, our approach uncovers the governing equation for the spread of abnormal tau proteins in mouse brains, enabling early prediction of tau occupation in each brain region and revealing distinct pathology dynamics in mutant mice. By learning interpretable stochastic dynamics of complex systems, our findings open new avenues for downstream applications such as control.
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Affiliation(s)
- Ting-Ting Gao
- MOE Key Laboratory of Advanced Micro-Structured Materials, and School of Physical Science and Engineering, Tongji University, Shanghai, P. R. China
- Shanghai Research Institute for Intelligent Autonomous Systems, National Key Laboratory of Autonomous Intelligent Unmanned Systems, MOE Frontiers Science Center for Intelligent Autonomous Systems, and Shanghai Key Laboratory of Intelligent Autonomous Systems, Tongji University, Shanghai, P. R. China
| | - Baruch Barzel
- Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
- Gonda Multidisciplinary Brain Research Center, Bar-Ilan University, Ramat-Gan, Israel
| | - Gang Yan
- MOE Key Laboratory of Advanced Micro-Structured Materials, and School of Physical Science and Engineering, Tongji University, Shanghai, P. R. China.
- Shanghai Research Institute for Intelligent Autonomous Systems, National Key Laboratory of Autonomous Intelligent Unmanned Systems, MOE Frontiers Science Center for Intelligent Autonomous Systems, and Shanghai Key Laboratory of Intelligent Autonomous Systems, Tongji University, Shanghai, P. R. China.
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2
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Malizia F, Corso A, Gambuzza LV, Russo G, Latora V, Frasca M. Reconstructing higher-order interactions in coupled dynamical systems. Nat Commun 2024; 15:5184. [PMID: 38890277 PMCID: PMC11189584 DOI: 10.1038/s41467-024-49278-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 05/30/2024] [Indexed: 06/20/2024] Open
Abstract
Higher-order interactions play a key role for the operation and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators.
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Affiliation(s)
- Federico Malizia
- Dipartimento di Fisica ed Astronomia, Università di Catania, Catania, Italy
- Network Science Institute, Northeastern University London, London, E1W 1LP, UK
| | - Alessandra Corso
- Department of Electrical Electronic and Computer Science Engineering, University of Catania, Catania, Italy
| | - Lucia Valentina Gambuzza
- Department of Electrical Electronic and Computer Science Engineering, University of Catania, Catania, Italy
| | - Giovanni Russo
- Department of Mathematics and Computer Science, University of Catania, Catania, Italy
| | - Vito Latora
- Dipartimento di Fisica ed Astronomia, Università di Catania, Catania, Italy
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
- INFN, Catania, Italy
- Complexity Science Hub, Josefstäadter Strasse 39, A 1080, Vienna, Austria
| | - Mattia Frasca
- Department of Electrical Electronic and Computer Science Engineering, University of Catania, Catania, Italy.
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Ma L, Qiu Z, Van Mieghem P, Kitsak M. Reporting delays: A widely neglected impact factor in COVID-19 forecasts. PNAS NEXUS 2024; 3:pgae204. [PMID: 38846778 PMCID: PMC11156234 DOI: 10.1093/pnasnexus/pgae204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 05/13/2024] [Indexed: 06/09/2024]
Abstract
Epidemic forecasts are only as good as the accuracy of epidemic measurements. Is epidemic data, particularly COVID-19 epidemic data, clean, and devoid of noise? The complexity and variability inherent in data collection and reporting suggest otherwise. While we cannot evaluate the integrity of the COVID-19 epidemic data in a holistic fashion, we can assess the data for the presence of reporting delays. In our work, through the analysis of the first COVID-19 wave, we find substantial reporting delays in the published epidemic data. Motivated by the desire to enhance epidemic forecasts, we develop a statistical framework to detect, uncover, and remove reporting delays in the infectious, recovered, and deceased epidemic time series. Using our framework, we expose and analyze reporting delays in eight regions significantly affected by the first COVID-19 wave. Further, we demonstrate that removing reporting delays from epidemic data by using our statistical framework may decrease the error in epidemic forecasts. While our statistical framework can be used in combination with any epidemic forecast method that intakes infectious, recovered, and deceased data, to make a basic assessment, we employed the classical SIRD epidemic model. Our results indicate that the removal of reporting delays from the epidemic data may decrease the forecast error by up to 50%. We anticipate that our framework will be indispensable in the analysis of novel COVID-19 strains and other existing or novel infectious diseases.
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Affiliation(s)
- Long Ma
- Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, GA 2600, The Netherlands
| | - Zhihao Qiu
- Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, GA 2600, The Netherlands
| | - Piet Van Mieghem
- Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, GA 2600, The Netherlands
| | - Maksim Kitsak
- Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, GA 2600, The Netherlands
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Murphy C, Thibeault V, Allard A, Desrosiers P. Duality between predictability and reconstructability in complex systems. Nat Commun 2024; 15:4478. [PMID: 38796449 PMCID: PMC11127975 DOI: 10.1038/s41467-024-48020-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 04/15/2024] [Indexed: 05/28/2024] Open
Abstract
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.
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Affiliation(s)
- Charles Murphy
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada.
| | - Vincent Thibeault
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada
| | - Antoine Allard
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada
| | - Patrick Desrosiers
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre de recherche CERVO, Québec, QC, G1J 2G3, Canada.
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Ding Y, Gao J, Magdon-Ismail M. Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares. Phys Rev E 2024; 109:034301. [PMID: 38632807 DOI: 10.1103/physreve.109.034301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 01/08/2024] [Indexed: 04/19/2024]
Abstract
In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equations to compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.
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Affiliation(s)
- Yanna Ding
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Jianxi Gao
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Malik Magdon-Ismail
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
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Tonnelier A. Exact solutions for signal propagation along an excitable transmission line. Phys Rev E 2024; 109:014219. [PMID: 38366484 DOI: 10.1103/physreve.109.014219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Accepted: 12/08/2023] [Indexed: 02/18/2024]
Abstract
A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.
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Affiliation(s)
- Arnaud Tonnelier
- Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
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Tavasoli A, Henry T, Shakeri H. A purely data-driven framework for prediction, optimization, and control of networked processes. ISA TRANSACTIONS 2023; 138:491-503. [PMID: 37037734 DOI: 10.1016/j.isatra.2023.03.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2022] [Revised: 03/12/2023] [Accepted: 03/12/2023] [Indexed: 06/16/2023]
Abstract
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here, we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior knowledge of the network structure and identifies the underlying dynamics solely using a collection of two-step snapshots of the states. This data-driven system identification is achieved by using the Koopman operator to find a low-dimensional representation of the dynamical patterns that evolve linearly. Further, we use the global linear Koopman model to solve critical control problems by applying to model predictive control (MPC)-typically, a challenging proposition when applied to large networks. We show that our proposed approach tackles this by converting the original nonlinear programming into a more tractable optimization problem that is both convex (quadratic programming) and with far fewer variables.
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Affiliation(s)
- Ali Tavasoli
- School of Data Science, University of Virginia, Charlottesville, 22904, VA, United States of America
| | - Teague Henry
- School of Data Science, University of Virginia, Charlottesville, 22904, VA, United States of America; Department of Psychology, University of Virginia, Charlottesville, 22904, VA, United States of America
| | - Heman Shakeri
- School of Data Science, University of Virginia, Charlottesville, 22904, VA, United States of America.
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Wu L, Yi L, Ren XL, Lü L. Predicting the Popularity of Information on Social Platforms without Underlying Network Structure. ENTROPY (BASEL, SWITZERLAND) 2023; 25:916. [PMID: 37372260 DOI: 10.3390/e25060916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Revised: 05/25/2023] [Accepted: 06/06/2023] [Indexed: 06/29/2023]
Abstract
The ability to predict the size of information cascades in online social networks is crucial for various applications, including decision-making and viral marketing. However, traditional methods either rely on complicated time-varying features that are challenging to extract from multilingual and cross-platform content, or on network structures and properties that are often difficult to obtain. To address these issues, we conducted empirical research using data from two well-known social networking platforms, WeChat and Weibo. Our findings suggest that the information-cascading process is best described as an activate-decay dynamic process. Building on these insights, we developed an activate-decay (AD)-based algorithm that can accurately predict the long-term popularity of online content based solely on its early repost amount. We tested our algorithm using data from WeChat and Weibo, demonstrating that we could fit the evolution trend of content propagation and predict the longer-term dynamics of message forwarding from earlier data. We also discovered a close correlation between the peak forwarding amount of information and the total amount of dissemination. Finding the peak of the amount of information dissemination can significantly improve the prediction accuracy of our model. Our method also outperformed existing baseline methods for predicting the popularity of information.
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Affiliation(s)
- Leilei Wu
- Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
- Alibaba Business School, Hangzhou Normal University, Hangzhou 311121, China
| | - Lingling Yi
- Tencent Technology (Shenzhen) Co., Ltd., Shenzhen 518000, China
| | - Xiao-Long Ren
- Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China
| | - Linyuan Lü
- Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
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