Dynamical Systems

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Overview

Dynamical systems describe how a system's state changes over time and explain behaviors such as equilibria, oscillations, attractors, bifurcations, and chaos. Researchers analyze these behaviors mathematically and learn models from data using approaches such as Koopman operators, neural ODEs, physics-informed networks, and structure-preserving Hamiltonian models. Applications range from forecasting Lorenz and pendulum dynamics to modeling reaction-diffusion processes, neural activity, and robot motion, often with control and safety guarantees. A central challenge is that accurate short-term predictions do not ensure faithful long-term behavior: learned models can drift, violate physical constraints, or fail to generalize to unseen regimes.

Latest papers

CardsList

482 papers56 papers in the last four weeks, up 19% on the four weeks before. 0.3% of all new papers.

  1. On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials

    Feb 16, 2026Rotem Mulayoff, Sebastian U. StichGradient Descent DynamicsStochastic Gradient Descent

    CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

  2. Preliminary sonification of ENSO using traditional Javanese gamelan scales

    Feb 16, 2026Sandy Hardian Susanto Herho, Rusmawan Suwarman, Nurjanna Joko Trilaksono +2SonificationChaotic Dynamical Systems

    Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA · School of Systems Science and Industrial Engineering, State University of New York (SUNY), Binghamton, NY 13902, USA · Ronin Institute for Independent Scholarship 2.0, Sacramento, CA 95816, USA +3

  3. Is Flow Matching Just Trajectory Replay for Sequential Data?

    Feb 9, 2026Soon Hoe Lim, Shizheng Lin, Michael W. Mahoney +1Flow MatchingTime Series Generation

    Department of Mathematics, KTH Royal Institute of Technology · Nordita, KTH Royal Institute of Technology and Stockholm University · Department of Statistics, University of California at Berkeley +2

  4. SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants

    Jan 30, 2026Santanu Subhash Rathod, Pietro Liò, Xiao ZhangFlow MatchingConditional Flow Matching

    CISPA Helmholtz Center for Information Security, Saarbrücken, Germany · Department of Computer Science and Technology, University of Cambridge, UK

  5. Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics

    Jan 29, 2026Winfried Ripken, Michael Plainer, Gregor Lied +5Dynamical SystemsFlow Map Learning

    Technical University Berlin · BIFOLD · Free University of Berlin +6

  6. Model-Free Output Feedback Stabilization via Policy Gradient Methods

    Jan 27, 2026Ankang Zhang, Ming Chi, Xiaoling Wang +1Dynamical SystemsPartially Observable RL

    School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China · College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

  7. Neural Particle Automata: Learning Self-Organizing Particle Dynamics

    Jan 22, 2026Hyunsoo Kim, Ehsan Pajouheshgar, Sabine Süsstrunk +2Neural Cellular AutomataDynamical Systems

    KAIST, South Korea · EPFL, Switzerland

  8. The Replicator-Optimization Mechanism: A Scale-Relative Formalism for Persistence-Conditioned Dynamics with a Conditional Consent-Friction Instantiation

    Jan 10, 2026Murad FarzullaDynamical SystemsReplicator Dynamics

    Dissensus, London, UK · King’s College London, London, UK

  9. Minimum distance classification for nonlinear dynamical systems

    Jan 7, 2026Dominique MartinezDynamical SystemsTime Series Classification

    Aix-Marseille University, CNRS, ISM, 13009 Marseille, France

  10. Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

    Jan 1, 2026Abhisek Ganguly, Santosh Ansumali, Sauro SucciDynamical SystemsNeural PDE Solvers

    Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, 560064, Karnataka, India · Italian Institute of Technology, Viale Regina Elena 291, 00161 Rome, Italy · University of Roma Tre, Italy +2

  11. Exact Flow Linear Attention: Exact Solution from Continuous-Time Dynamics

    Dec 14, 2025Jingdi Lei, Di Zhang, Soujanya PoriaDynamical SystemsLinear Attention

    Nanyang Technological University · Fudan University

  12. Tracking large chemical reaction networks and rare events by neural networks

    Dec 11, 2025Jiayu Weng, Xinyi Zhu, Jing Liu +3Dynamical SystemsNeural Surrogate Modeling

    Institute of Data Science, University of Hong Kong, Hong Kong · Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China · School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China +6

  13. Symmetric Linear Dynamical Systems are Learnable from Few Observations

    Dec 5, 2025Minh Vu, Andrey Y. Lokhov, Marc VuffrayDynamical SystemsParameter Estimation

    Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

  14. When is a System Discoverable from Data? Discovery Requires Chaos

    Nov 12, 2025Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3Dynamical SystemsNonlinear System Identification

    University of Cambridge · LMU Munich and Munich Center for Machine Learning (MCML) · IBM Research

  15. Nonlinear Dynamics In Optimization Landscape of Shallow Neural Networks with Tunable Leaky ReLU

    Oct 29, 2025Jingzhou LiuShallow Neural NetworksDynamical Systems

  16. Simulation-free Structure Learning for Stochastic Population Dynamics

    Oct 18, 2025Noah El Rimawi-Fine, Adam Stecklov, Lucas Nelson +4Dynamical SystemsCausal Structure Learning

    McGill University · Mila – Quebec AI Institute · AITHYRA +5

  17. Neural non-canonical Hamiltonian dynamics for long-time simulations

    Oct 2, 2025Clémentine Courtès, Emmanuel Franck, Michael Kraus +2Dynamical SystemsNonlinear System Identification

    IRMA, MACARON · Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René Descartes 672000 Strasbourg, France. · INRIA Nancy-Grand Est, MACARON Project, Strasbourg, France. +5

  18. Data-efficient Kernel Methods for Learning Hamiltonian Systems

    Sep 21, 2025Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi +2Dynamical SystemsNonlinear System Identification

    Department of Computing and Mathematical Sciences, Caltech, CA, USA. · Beyond Limits, CA, USA. · The Alan Turing Institute, London, UK. +1

  19. Universal Learning of Nonlinear Dynamics

    Aug 16, 2025Evan Dogariu, Anand Brahmbhatt, Elad HazanDynamical SystemsNonlinear System Identification

    Courant Institute of Mathematical Sciences, New York University · Princeton University

  20. Diagrams-to-Dynamics (D2D): Exploring Causal Loop Diagram Leverage Points under Uncertainty

    Jul 30, 2025Jeroen F. Uleman, Loes Crielaard, Leonie K. Elsenburg +4Dynamical SystemsCausal Intervention

    Copenhagen Health Complexity Center, University of Copenhagen, Copenhagen, Denmark. · Department of Public and Occupational Health, Amsterdam UMC University of Amsterdam, Amsterdam, The Netherlands. · Center for Urban Mental Health, University of Amsterdam, Amsterdam, The Netherlands. +4

  21. Artifacts of Numerical Integration in Learning Dynamical Systems

    Jul 19, 2025Bing-Ze Lu, Richard TsaiNumerical IntegrationDynamical Systems

    National Chung Cheng University, Taiwan · The University of Texas at Austin, USA

  22. Dynamical stability for dense patterns in attractor neural networks

    Jul 14, 2025Uri Cohen, Máté LengyelNeural Network MemorizationAssociative Memory

    Computational and Biological Learning Lab, Department of Engineering, University of Cambridge, Cambridge, UK · Center for Cognitive Computation, Department of Cognitive Science, Central European University, Budapest, Hungary

  23. Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models

    Jun 25, 2025Xinghao Dong, Huchen Yang, Jin-Long WuDynamical SystemsLatent Diffusion Models

    Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

  24. Regularity and Stability Properties of Selective SSMs with Discontinuous Gating

    May 16, 2025Nikola Zubić, Davide ScaramuzzaDynamical SystemsSelective SSMs

    Robotics and Perception Group University of Zurich

  25. A Hybrid ABM-PDE Framework for Real-World Infectious Disease Simulations

    Apr 11, 2025Kristina Kehrer, Tim O. F. ConradDynamical SystemsAgent-Based Modeling

    Zuse Institute Berlin Berlin, 14195

  26. No Undesirable Equilibria, No Collisions: Combining Modulation and Control Barrier Functions for Liveness and Safety in Dynamic Collision Avoidance

    Feb 20, 2025Yifan Xue, Nadia FigueroaControl Barrier FunctionsSafety-Critical Control

    the Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 USA

  27. Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs

    Feb 1, 2025Bongseok Kim, Haoyang Zheng, Michael Penwarden +1Dynamical SystemsSurrogate Modeling

    School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, 47907, IN, USA. · Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, 47907, IN, USA.

  28. Projected Neural Differential Equations for Learning Constrained Dynamics

    Oct 31, 2024Alistair White, Anna Büttner, Maximilian Gelbrecht +4Dynamical SystemsNeural ODEs

    Munich Climate Center and Earth System Modelling Group, Department of Aerospace and Geodesy, School of Engineering and Design, Technical University of Munich, Munich, Germany · Potsdam Institute for Climate Impact Research, Potsdam, Germany · California Institute of Technology, Pasadena, California, USA +4

  29. Automated Discovery of Operable Dynamics from Videos

    Oct 14, 2024Kuang Huang, Dong Heon Cho, Boyuan ChenDynamical SystemsLatent Dynamics Modeling

    Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, New York, 10027, NY, USA. · Department of Computer Science, Duke University, 308 Research Dr., Durham, 27705, NC, USA. · Department of Mechanical Engineering and Material Science, Duke University, 121 Hudson Hall, Durham, 27708, NC, USA. +1

  30. Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes

    Jun 7, 2024Si Yi Meng, Antonio Orvieto, Daniel Yiming Cao +1Dynamical SystemsLogistic Regression

    Department of Computer Science Cornell University Ithaca, NY, USA · ELLIS Institute Tübingen MPI for Intelligent Systems Tübingen AI Center, Germany