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. Fractals made Practical: Denoising Diffusion as Partitioned Iterated Function Systems

    Mar 13, 2026Ann DoomsDiffusion-Based DenoisingDiffusion Models

    Department of Mathematics & Data Science Vrije Universiteit Brussel Pleinlaan 2, 1050 Brussels, BELGIUM

  2. Chemical Reaction Networks Learn Better than Spiking Neural Networks

    Mar 12, 2026Sophie Jaffard, Ivo F. SbalzariniClassificationDynamical Systems

    Max Planck Institute of Molecular Cell Biology and Genetics Center for Systems Biology Dresden Dresden, Germany · Dresden University of Technology, Faculty of Computer Science Max Planck Institute of Molecular Cell Biology and Genetics Center for Systems Biology Dresden Dresden, Germany

  3. Feedback-Coupled Memory Systems: A Dynamical Model for Adaptive Coordination

    Mar 12, 2026Stefano GrassiCritical Slowing DownMulti-Agent Coordination

    Bangkok University, Phahonyothin Rd, Khlong Nueng, Khlong Luang District, Pathum Thani 12120, Thailand

  4. Factorized Neural Implicit DMD for Parametric Dynamics

    Mar 11, 2026Siyuan Chen, Zhecheng Wang, Yixin Chen +4Dynamical SystemsNeural Surrogate Modeling

    Department of Computer Science, University of British Columbia, Vancouver, Canada · Department of Computer Science, University of Toronto, Toronto, Canada

  5. MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems

    Mar 11, 2026Heikki Haario, Zhi-Song Liu, Martin Simon +1Ordinary Differential EquationsUncertainty Quantification

    Lappeenranta-Lahti University of Technology LUT, Lahti, Finland · Frankfurt University of Applied Sciences, Frankfurt am Main, Germany · University of Huddersfield, Huddersfield, United Kingdom

  6. JEDI: Jointly Embedded Inference of Neural Dynamics

    Mar 11, 2026Anirudh Jamkhandi, Ali Korojy, Olivier Codol +2Latent Dynamics ModelingDynamical Systems

    Mila - Quebec AI Institute · Université de Montréal

  7. Walking on Rough Terrain with Any Number of Legs

    Mar 10, 2026Zhuoyang Chen, Xinyuan Wang, Shai RevzenLegged RoboticsRobot Locomotion

    The authors are with the University of Michigan, Ann Arbor, MI 48109, USA.

  8. Exploring Collatz Dynamics with Human-LLM Collaboration

    Mar 10, 2026Edward Y. ChangDynamical Systems

    Computer Science, Stanford University · QuadriumAI

  9. STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching

    Mar 9, 2026Prakrut Kotecha, Ganga Nair B, Shishir KolathayaLagrangian Neural NetworksRobot Dynamics Learning

    the Robert Bosch Center for Cyber-Physical Systems, Indian Institute of Science, Bengaluru · the Robert Bosch Center for Cyber-Physical Systems and the Department of Computer Science & Automation, Indian Institute of Science, Bengaluru

  10. Learning Quadruped Walking from Seconds of Demonstration

    Mar 7, 2026Ruipeng Zhang, Hongzhan Yu, Ya-Chien Chang +3Robot Imitation LearningData-Efficient Robot Learning

    University of California, San Diego

  11. VertiAdaptor: Online Kinodynamics Adaptation for Vertically Challenging Terrain

    Mar 6, 2026Tong Xu, Chenhui Pan, Aniket Datar +1Dynamical SystemsOnline System Identification

    Department of Computer Science, George Mason University

  12. Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics

    Mar 6, 2026Yaojun Li, Yulong Yang, Christine Allen-BlanchetteHamiltonian Neural NetworksDynamical Systems

    Princeton University, USA

  13. Random Quadratic Form on a Sphere: Synchronization by Common Noise

    Mar 6, 2026Maximilian Engel, Anna ShalovaStochastic Differential EquationsDynamical Systems

    Korteweg-de Vries Institute for Mathematics, University of Amsterdam · Department of Mathematics and Computer Science, FU Berlin

  14. Behavior-dLDS: A decomposed linear dynamical systems model for neural activity partially constrained by behavior

    Mar 5, 2026Eva Yezerets, En Yang, Misha B. Ahrens +1Latent Dynamics ModelingDynamical Systems

    Department of Biomedical Engineering Center for Imaging Science Johns Hopkins University · Department of Biology University of North Carolina · Janelia Research Campus Howard Hughes Medical Institute

  15. Curve-Induced Dynamical Systems on Riemannian Manifolds and Lie Groups

    Mar 5, 2026Saray Bakker, Martin Schonger, Tobias Löw +2Dynamical SystemsRobot Motion Generation

    Delft University of Technology, The Netherlands · Idiap Research Institute, Switzerland · École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

  16. Latent Particle World Models: Self-supervised Object-centric Stochastic Dynamics Modeling

    Mar 4, 2026Tal Daniel, Carl Qi, Dan Haramati +5World Model LearningObject-Centric World Models

    Carnegie Mellon University · UT Austin · Brown University +2

  17. Lyapunov Stability of Stochastic Vector Optimization: Theory and Numerical Implementation

    Mar 4, 2026Thiago Santos, Sebastiao XavierMulti-Objective OptimizationStochastic Differential Equations

    Department of Mathematics, Federal University of Ouro Preto, UFOP, Ouro Preto, Brazil

  18. A Dynamical Theory of Sequential Retrieval in Input-Driven Hopfield Networks

    Mar 3, 2026Simone Betteti, Giacomo Baggio, Sandro ZampieriHopfield NetworksAssociative Memory

    The Italian Institute of Artificial Intelligence for Industry · Department of Information Engineering, Università degli Studi di Padova

  19. Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians

    Mar 2, 2026Yunhao Fan, Gia-Wei ChernGraph Neural NetworksHamiltonian Dynamics

    Department of Physics, University of Virginia, Charlottesville, VA 22904, USA

  20. CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning

    Mar 2, 2026Pratik Jawahar, Maurizio PieriniSymplectic RNNsHamiltonian Neural Networks

    University of Manchester · CERN

  21. Path Integral Particle Filtering for Hybrid Systems via Saltation Matrices

    Mar 1, 2026Karthik Shaji, Sreeranj Jayadevan, Bo Yuan +2Particle FilteringRobot State Estimation

    Graduate Student, Daniel Guggenheim School of Aerospace Engineering · MathWorks · PlusAI +1

  22. Solving stiff dark matter equations via Jacobian Normalization with Physics-Informed Neural Networks

    Feb 25, 2026M. P. Bento, H. B. Câmara, J. R. Rocha +1Physics-Informed MLDynamical Systems

    Departamento de Física and CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal · Institute of Experimental and Applied Physics, Czech Technical University in Prague, Prague 160 00, Czech Republic

  23. Systematic Analysis of Coupling Effects on Closed-Loop and Open-Loop Performance in Aerial Continuum Manipulators

    Feb 21, 2026Niloufar Amiri, Shayan Sepahvand, Iraj Mantegh +1Continuum Robot ControlAerial Manipulation

    Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada · Aerospace Research Center, National Research Council of Canada (NRC), Montreal, QC H3T 2B2, Canada

  24. Transformers for dynamical systems learn transfer operators in-context

    Feb 21, 2026Anthony Bao, Jeffrey Lai, William GilpinIn-Context LearningDynamical Systems

    Department of Electrical & Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA · The Oden Institute, The University of Texas at Austin, Austin, Texas 78712, USA · Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA

  25. Deepmechanics

    Feb 20, 2026Abhay Shinde, Aryan Amit Barsainyan, Jose Siguenza +3Symplectic RNNsLagrangian Neural Networks

    Deep Forest Sciences, Mumbai, Maharashtra, India · Deep Forest Sciences, Bengaluru, Karnataka, India · Deep Forest Sciences, Palo alto, California, USA +1

  26. Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling

    Feb 18, 2026Daniel Durstewitz, Christoph Jürgen Hemmer, Florian Hess +2Time Series ModelingTime Series Forecasting

    Dept. of Theoretical Neuroscience, Central Institute of Mental Health, Mannheim, Germany · Faculty of Physics & Astronomy, Heidelberg Univ., Heidelberg, Germany · Interdisciplinary Center for Scientific Computing, Heidelberg, Germany

  27. Evolutionary Systems Thinking: From Equilibrium Models to Open-Ended Adaptive Dynamics

    Feb 17, 2026Dan AdlerOpen-Ended EvolutionDynamical Systems

  28. Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry

    Feb 17, 2026Deniz Kucukahmetler, Maximilian Jean Hemmann, Julian Mosig von Aehrenfeld +4Neural Representation GeometryLatent Space Alignment

    Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany · School of Embedded Composite Artificial Intelligence (SECAI), Dresden/Leipzig, Germany · Leipzig University, Leipzig, Germany +2

  29. Continuous-Time Piecewise-Linear Recurrent Neural Networks

    Feb 17, 2026Alena Brändle, Lukas Eisenmann, Florian Götz +1Recurrent Neural NetworksDynamical Systems

    Dept. of Theoretical Neuroscience, Central Institute of Mental Health (CIMH), Mannheim, Germany · Faculty of Physics and Astronomy, Heidelberg University · Hector Institute for Artificial Intelligence in Psychiatry, CIMH +2

  30. Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks

    Feb 16, 2026Ramón Nartallo-Kaluarachchi, Renaud Lambiotte, Alain GorielyRecurrent Neural NetworksDynamical Systems

    Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, United Kingdom · Centre for Eudaimonia and Human Flourishing, University of Oxford, 7 Stoke Pl, Oxford, OX3 9BX, United Kingdom · Complexity Science Hub, Metternichgasse 8, Vienna, 1030, Austria