Chaotic Dynamical Systems

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Overview

Chaotic dynamical systems are deterministic systems in which small differences in initial conditions can quickly separate trajectories, even when long-term statistical patterns remain stable. Researchers study attractors, Lyapunov exponents, bifurcations, and how these systems can be predicted, controlled, or inferred from limited noisy observations. Common approaches include equation discovery with sparse regression and Bayesian methods, neural ODEs, reservoir and Koopman models, and physics-informed learning. A central challenge is that accurate short-term forecasts do not guarantee faithful long-term dynamics: models must also reproduce invariant statistics, instability, and rare events.

Latest papers

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47 papers7 papers in the last four weeks, up 133% on the four weeks before. 0.0% of all new papers.

  1. Self-Organization from Constrained Geometric Radiation

    Oct 7, 2026Ming LeiChaotic Dynamical Systems

    School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai, 200240, China.

  2. Lyapunov-Inspired LyRIC Activation and GLARE Attention in Chaos-Guided State Space Modeling for EMG-To-Speech (ETS) Synthesis

    Oct 6, 2026Sajid Fardin Dipto, Tarikul Islam Tamiti, Luke Baja-Ricketts +2State Space ModelsChaotic Dynamical Systems

    Department of Cyber Security Engineering George Mason University Fairfax, VA, USA

  3. A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63

    Oct 5, 2026João Böger, Simon Driscoll, Niccolò Zagli +2Surrogate ModelingChaotic Dynamical Systems

    Department of Technology, Management and Economics Technical University of Denmark Kongens Lyngby, 2800, DK · Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge, CB3 0WA, UK · School of Computing and Mathematical Sciences University of Leicester Leicester, LE1 7RH, UK +1

  4. Do Neural PDE Solvers Learn the Right Dynamics?

    Oct 3, 2026Haonan Li, Yue Song, Bin Yang +1Neural PDE SolversDynamical Systems

    Center for Combustion Energy, Tsinghua University · College of AI, Tsinghua University · Department of Mechanical Engineering, University College London

  5. Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics

    Oct 2, 2026Lufang Chiang, Jiachen Yao, Thomas Y. L. Lin +1Chaotic Time-Series PredictionChaotic Dynamical Systems

    National Taiwan University · California Institute of Technology · University of Washington

  6. Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers

    Sep 30, 2026Yilun Liu, Yi Zhang, Ganyu Wu +5Dynamical SystemsChaotic Dynamical Systems

    Ludwig Maximilian University of Munich · Munich Center for Machine Learning · Technical University of Munich

  7. Massively Parallel Reinforcement Learning with a Chaotic Reconfigurable Clockless Chip

    Sep 28, 2026Eric Oliveira-Gomes, Damien RontaniReinforcement LearningGPU-Accelerated RL

    CentraleSup´elec and Universit´e de Lorraine, LMOPS UR4423 Laboratory, Metz F-57070, France

  8. Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events

    Sep 25, 2026Isabella S. Thiel, Juan Bello-Rivas, Yannis G. Kevrekidis +1Rare-Event EstimationChaotic Time-Series Prediction

    Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139 · Department of Applied Mathematics and Statistics, Johns Hopkins University Baltimore, MD 21218 · Department of Chemical and Biomolecular Engineering, Johns Hopkins University Baltimore, MD 21218

  9. Nonequilibrium Phases of Repulsive Self-Attention: Chaos, Attention Condensation, and Emergent Locality

    Sep 23, 2026Qucheng Gao, Zuyi Yang, Xiao ChenSelf-AttentionChaotic Dynamical Systems

    Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA

  10. Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

    Sep 1, 2026Ling-Wei Kong, Ying-Cheng LaiDynamical SystemsReservoir Computing

    Department of Computational Biology, Cornell University, Ithaca, NY 14850, USA · School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA · Department of Physics, Arizona State University, Tempe, Arizona 85287, USA

  11. Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems

    Aug 29, 2026Aidan Li, Uday Kiran Reddy Tadipatri, Mahan Fathi +2Koopman Operator LearningDynamical Systems

    Chandar Research Lab · Mila – Quebec AI Institute · Université de Montréal +4

  12. Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?

    Aug 26, 2026Pedram Hassanzadeh, Weidong Li, Y. Qiang Sun +4Weather ForecastingChaotic Time-Series Prediction

    Department of Geophysical Sciences, University of Chicago, Chicago, USA · Committee on Computational and Applied Mathematics, University of Chicago, Chicago, USA. · Data Science Institute, University of Chicago, Chicago, USA. +3

  13. Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems

    Aug 23, 2026Zhou Fang, Gianmarco MengaldoChaotic Time-Series PredictionAdaptive Loss Weighting

    Department of Mechanical Engineering National University of Singapore Singapore

  14. Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics

    Aug 20, 2026Andrei Velichko, Viet-Thanh PhamRare-Event PredictionChaotic Time-Series Prediction

    Institute of Physics and Technology, Petrozavodsk State University, 33 Lenin Ave., Petrozavodsk, 185910, Russia · Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

  15. Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics

    Aug 17, 2026Conrad Ainslie, Pedram Hassanzadeh, Michael W. Mahoney +1Neural Network StabilityNeural Surrogate Modeling

    Department of Applied Mathematics, University of California, Santa Cruz, Santa Cruz, 95064, CA · Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637 · Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL 60637 +3

  16. Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles

    Aug 6, 2026Andrei Velichko, N'Gbo N'Gbo, Viet-Thanh PhamChaotic Dynamical SystemsLyapunov Exponent Estimation

    Institute of Physics and Technology, Petrozavodsk State University, 33 Lenina Prospekt, Petrozavodsk, Republic of Karelia, 185910, Russia · School of Science and Engineering, International University of Grand-Bassam, Route de Bonoua, BP 564, Grand-Bassam, Cˆote d’Ivoire · Laboratory for Intelligence and Mathematics (LIMAs), Route de Bonoua, BP 564, Grand-Bassam, Cˆote d’Ivoire +1

  17. Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks

    Jul 31, 2026Jaesung ChoiNeural Surrogate ModelingDynamical Systems

    Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

  18. Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

    Jul 26, 2026Nikolaos Kollias, Nikolaos MatzakosDynamical SystemsChaotic Dynamical Systems

    School of Science and Technology, Hellenic Open University, Athens, Greece. · School of Pedagogical and Technological Education (ASPETE), Athens, Greece.

  19. Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos

    Jul 23, 2026Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski +2Dynamical SystemsGame Theory

    Department of Mathematics, Krakow University of Economics, Rakowicka 27, 31-510 Kraków, Poland · Chula Intelligent and Complex Systems Lab, Department of Physics, Faculty of Science, Chulalongkorn University,Bangkok 10330, Thailand · Department of Mathematical Sciences, Indiana University Indianapolis,402 N. Blackford Street, Indianapolis, Indiana 46202, USA +1

  20. Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression

    Jun 30, 2026Max Kreider, John Harlim, Daning HuangKernel Ridge RegressionKernel Regression

    Department of Mathematics The Pennsylvania State University, University Park, PA 16802, USA · Department of Mathematics, Institute for Computational and Data Sciences The Pennsylvania State University, University Park, PA 16802, USA · Department of Aerospace Engineering The Pennsylvania State University, University Park, PA 16802, USA

  21. Scalar Representations of Neural Network Training Dynamics

    Jun 29, 2026Pedro Jiménez-González, Miguel C. Soriano, Lucas LacasaNeural Network OptimizationChaotic Dynamical Systems

    Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain

  22. Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching

    Jun 23, 2026Peiyan Hu, Jian Zhang, Jiashu Pan +6Simulation-Based InferenceConditional Flow Matching

    Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. · Department of Artificial Intelligence, School of Engineering, Westlake University, Hangzhou, Zhejiang, 310030, China. · School of Astronomy and Space Sciences, Chinese Academy of Sciences, Beijing, 100049, China. +4

  23. The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings

    Jun 22, 2026Kanishk AwadhiyaSpectral BiasChaotic Dynamical Systems

    Independent Researcher

  24. LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor

    Jun 21, 2026Ruslan GokhmanTemporal Convolutional NetworksChaotic Dynamical Systems

    Yeshiva University

  25. Divide-and-Conquer Modeling for the CTF-4-Science Lorenz Benchmark

    Jun 8, 2026Shundong LiForecasting BenchmarksChaotic Dynamical Systems

    Worcester Polytechnic Institute Worcester, MA, USA

  26. Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series

    Jun 5, 2026S. V. Manivelan, Andrei Velichko, I. ManimehanDynamical SystemsChaotic Dynamical Systems

    Department of Physics, M. R. Government Arts College (Affiliated to Bharathidasan University, Tiruchirappalli), Mannargudi, 614 001, Tamilnadu, India. · Institute of Physics and Technology, Petrozavodsk State University, Petrozavodsk, 185910, Russia.

  27. Learning Chaotic Dynamics through Second-Order Geometric Supervision

    Jun 1, 2026Shinhoo Kang, Hai V. Nguyen, Tan Bui-ThanhNonlinear System IdentificationChaotic Dynamical Systems

    Department of Computer Science and Software Engineering, Korea University, Sejong 30019, KR · Department of Aerospace Engineering and Engineering Mechanics, The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 2026 TX, USA

  28. The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling

    May 29, 2026Andre Herz, Matthijs Pals, Daniel Durstewitz +1Dynamical SystemsSurrogate Modeling

    1Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany · Faculty of Mathematics and Computer Science, Heidelberg University, Germany · 3Dept. of Theoretical Neuroscience, Central Institute of Mental Health (CIMH), Mannheim, Germany +3

  29. On Distributional Reinforcement Learning in Chaotic Dynamical Systems

    May 28, 2026James Rudd-Jones, Mirco Musolesi, María Pérez-OrtizDistributional RLReinforcement Learning

    Centre for Artificial Intelligence Department of Computer Science University College London London, UK · Department of Computer Science and Engineering, University of Bologna Bologna, Italy

  30. Model discovery for dynamical systems with complex-valued product units

    May 26, 2026Martin Brückmann, Babette Dellen, Uwe JaekelNonlinear System IdentificationComplex-Valued Neural Networks

    Department of Mathematics, Informatics, and Technology, RheinAhrCampus Remagen University of Applied Sciences Koblenz Joseph-Rovan-Allee 2, 53424 Remagen, Germany