Predicting Dynamics of Ultra-Large Complex Systems by Inferring Governing Equations
Southeast University（东南大学）；Queen Mary University of London（伦敦玛丽女王大学）；Università di Catania and INFN（卡塔尼亚大学及国家核物理研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；Fudan University（复旦大学）
Predicting the behavior of ultra-large complex systems, from climate to biological and technological networks, is a central unsolved challenge. Existing approaches face a fundamental trade-off: equation discovery methods provide interpretability but fail to scale, while neural networks scale but operate as black boxes and often lose reliability over long times. Here, we introduce the Sparse Identification Graph Neural Network, a framework that overcome this divide by allowing to infer the governing equations of large networked systems from data. By defining symbolic discovery as edge-level information, SIGN decouples the scalability of sparse identification from network size, enabling efficient equation discovery even in large systems. SIGN allows to study networks with over 100,000 nodes while remaining robust to noise, sparse sampling, and missing data. Across diverse benchmark systems, including coupled chaotic oscillators, neural dynamics, and epidemic spreading, it recovers governing equations with high precision and sustains accurate long-term predictions. Applied to a data set of time series of temperature measurements in 71,987 sea surface positions, SIGN identifies a compact predictive network model and captures large-scale sea surface temperature conditions up to two years in advance. By enabling equation discovery at previously inaccessible scales, SIGN opens a path toward interpretable and reliable prediction of real-world complex systems.
Extending Deep Knowledge Tracing: Inferring Interpretable Knowledge and Predicting Post-System Performance
Graduate School of Education, University of Pennsylvania（宾夕法尼亚大学教育研究生院）；Human-Computer Interaction Institute, Carnegie Mellon University（卡内基梅隆大学人机交互研究所）
Inferring hidden forcing in a biological oscillator using Kolmogorov-Arnold networks
Universidad de Buenos Aires（布宜诺斯艾利斯大学）；CONICET - Universidad de Buenos Aires（阿根廷国家科研委员会-布宜诺斯艾利斯大学）；Instituto de Física Interdisciplinaria y Aplicada (INFINA)（跨学科与应用物理研究所（INFINA））
Feedback System Neural Networks for Inferring Causality in Directed Cyclic Graphs
University of Bergen（卑尔根大学）；isee systems inc.（isee系统公司）
本文提出了一种新的因果网络学习算法（FSNN，Feedback System神经网络），它是在构造和分析非线性常微分方程组的基础上提出的。所构建的系统提供了对负责生成动态系统的过去和潜在未来行为的机制的洞察。它也可以用真实的系统变量来解释，提供了一个整体的，因果准确的，系统的理解现实生活中的相互作用，控制观察到的现象。本文演示了一个n维常微分方程模型，可以参数化，以适应测量数据，使用标准的数值优化技术的生成。该模型利用前馈人工神经网络来捕捉非线性，但在复杂系统中的因果关系网络是一个简约和可解释的表示。所生成的模型可以容易且快速地进行实验和分析，以使用循环重要方法（Schoenberg et. al 2019）。该方法的实用性和适用性的演示给出，表明它产生一个准确的，因果关系正确的模型为三状态，非线性，复杂的动态系统的已知来源。推广到其他动态系统与其他数据源，然后讨论。
Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes
W. M. Keck Science Department of Pitzer, Scripps, and Claremont McKenna College（皮泽学院、斯克里普斯学院和克莱蒙特·麦肯纳学院W.M.凯克科学系）；University of California at Davis（加州大学戴维斯分校）
Geometry-physics confounding impairs PDE learning across varying domains
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Nanjing Tech University（南京工业大学）；The Hong Kong Polytechnic University（香港理工大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
On Predicting Sociodemographics from Mobility Signals
Department of Civil and Environmental Engineering, University of Washington（土木与环境工程系，华盛顿大学）；Department of Technology, Management and Economics, Technical University of Denmark（技术、管理与经济系，丹麦技术大学）
Drug response prediction by inferring pathway-response associations with Kernelized Bayesian Matrix Factorization
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；Aalto University（阿尔托大学）；Institute for Molecular Medicine Finland FIMM（芬兰分子医学研究所）；University of Helsinki（赫尔辛基大学）；Science for Life Laboratory（生命科学实验室）；Karolinska Institutet（卡罗林斯卡学院）；University of Turku（图尔库大学）
Discovering equations from data: symbolic regression in dynamical systems
Institute of Sciences Mathematics and Computation, Universidade de São Paulo-Campus de São Carlos（数学与计算科学研究院，圣保罗大学-萨o卡洛斯校区）；Statistic Department, State University of Maringá（统计系，马林加州立大学）；Department of Mathematics Applied and Statistics, Institute of Sciences Mathematics and Computation, Universidade de São Paulo-Campus de São Carlos（应用数学与统计系，数学与计算科学研究院，圣保罗大学-萨o卡洛斯校区）
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
Brown University（布朗大学）；Technische Universität Ilmenau（伊尔默瑙工业大学）
Structure-Aware Variational Learning of a Class of Generalized Diffusions
School of Mathematics, South China University of Technology（华南理工大学数学学院）；Department of Applied Mathematics, Illinois Institute of Technology（伊利诺伊理工学院应用数学系）；School of Computational Science and Engineering, Georgia Institute of Technology（佐治亚理工学院计算科学与工程学院）
