Chaotic Time-Series Prediction

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers
Sep 30, 2026Yilun Liu, Yi Zhang, Ganyu Wu +5Dynamical Systems Chaotic Dynamical Systems
Ludwig Maximilian University of Munich · Munich Center for Machine Learning · Technical University of Munich
Context-dependent time-series prediction via HyperReservoirs
Sep 28, 2026Kohei Tsuchiyama, Takatomo Mihana, Ryoichi Horisaki +1Time Series Forecasting Reservoir Computing
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems
Jul 30, 2026Illia HorenkoScientific ML Feature Selection
Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.
fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture
Jul 20, 2026Charles Bokor, Mark Cary, Denise Morrey +1Koopman Operator Learning Nonlinear System Identification
School of Engineering, Computing and Mathematics Oxford Brookes University Oxford OX33 1HX, UK · Department of Aeronautical and Automotive Engineering Loughborough University Loughborough LE11 3TU, UK
Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting
Jul 20, 2026Yao Du, Xingang WangLyapunov Stability Reservoir Computing
School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China
A Quantum Reservoir Architecture for Chaotic Forecasting and a Test of Whether Its High Dimension Helps
Jul 8, 2026Tushar PandeyReservoir Computing Quantum Reservoir Computing
Texas A&M University, College Station, TX, USA
The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings
Jun 22, 2026Kanishk AwadhiyaSpectral Bias Chaotic Dynamical Systems
Independent Researcher
Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos
Jun 22, 2026Nima DehghaniEvolutionary Optimization Reservoir Computing
Department of Physics, MIT · McGovern Institute for Brain Research, MIT
LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor
Jun 21, 2026Ruslan GokhmanTemporal Convolutional Networks Chaotic Dynamical Systems
Yeshiva University
Neural dynamical systems on ferroelectric compute-in-memory for real-time forecasting
Jun 15, 2026Keshava Katti, Adithya Selvakumar, Pratik Chaudhari +1Efficient Neural Network Inference Dynamical Systems
Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
CIWI-CKT: Chaos-Informed Wave Interference Feature Fusion and Cross-City Knowledge Transfer for Traffic Flow Forecasting
Jun 14, 2026Abdul Joseph Fofanah, Lian Wen, David Chen +1Meta-Learning Few-Shot Learning
School of Information and Communication Technology, Griffith University, Brisbane, 4111, Australia · School of Information Engineering, Chang’an University, Xi’an, China
Divide-and-Conquer Modeling for the CTF-4-Science Lorenz Benchmark
Jun 8, 2026Shundong LiForecasting Benchmarks Chaotic Dynamical Systems
Worcester Polytechnic Institute Worcester, MA, USA
Metric-Aware Hybrid Forecasting for the CTF4Science Lorenz Challenge
Jun 2, 2026Cen LuTime Series Forecasting Forecasting Benchmarks
EPFL & Idiap Research Institute · Switzerland
Learning Chaotic Dynamics through Second-Order Geometric Supervision
Jun 1, 2026Shinhoo Kang, Hai V. Nguyen, Tan Bui-ThanhNonlinear System Identification Chaotic 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
Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
May 29, 2026Markus GrossKoopman Operator Learning Nonlinear System Identification
Institute for AI Safety and Security, German Aerospace Center (DLR), Sankt Augustin and Ulm, Germany
Adaptive Reservoir Computing for Multi-Scenario Chaotic System Forecasting
May 27, 2026Shadmehr Zaregarizi, Khashayar YavariDynamic Neural Networks Forecasting Benchmarks
Politecnico di Torino Turin, Italy
A comparative study of accuracy and rollout stability of temporal surrogate models
May 24, 2026Rajarshi BiswasNeural Surrogate Modeling Long-Term Time Series Forecasting
Cargill Inc. Wayzata, MN 55391, USA
FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series
May 17, 2026Andrei Velichko, N'Gbo N'Gbo, Bruno Carpentieri +1Time Series Forecasting Chaotic Dynamical Systems
Institute of Physics and Technology, Petrozavodsk State University, Petrozavodsk, Russia · School of Science and Engineering, International University of Grand Bassam, Grand Bassam, Cote d’Ivoire · Faculty of Engineering, Free University of Bozen-Bolzano, Bolzano, Italy +2
QuChaTeR: A Hybrid Quantum-Chaotic Temporal Framework for Earthquake Prediction
May 14, 2026Emir Kaan ÖzdemirHybrid Quantum-Classical ML Spatiotemporal Forecasting
Istanbul Erkek High School Ministry of National Education Istanbul, Türkiye · Ministry of National Education
ChaosNetBench: Benchmarking Spatio-Temporal Graph Neural Networks on Chaotic Lattice Dynamics
May 10, 2026Henok Tenaw Moges, Charalampos Skokos, Deshendran MoodleyForecasting Benchmarks Synthetic Benchmark Generation
Centre for Artificial Intelligence Research (CAIR) University of Cape Town, Cape Town, South Africa · Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics University of Cape Town, Cape Town, South Africa
Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics
Apr 28, 2026Andre Herz, Daniel Durstewitz, Georgia KoppeNeural Surrogate Modeling Dynamical Systems
Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany · Dept. of Theoretical Neuroscience, Central Institute of Mental Health (CIMH), Mannheim, Germany · Hector Institute for AI in Psychiatry and Dept. of Psychiatry and Psychotherapy, CIMH, Mannheim, Germany +1
An architectural capacity ceiling, not a barren plateau: why a fixed-encoding variational quantum circuit cannot fit the Lorenz-63 attractor
Apr 26, 2026Tushar PandeyVariational Quantum Circuits Physics-Informed ML
Texas A&M University, College Station, TX 77843, USA
Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs
Apr 23, 2026Mahadev Sunil Kumar, Adarsh GanesanDynamical Systems Reservoir Computing
Amrita School of Computing, Amrita Vishwa Vidyapeetham, Kollam, India 690525 · Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani – Dubai Campus, Dubai, United Arab Emirates 345055
A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
Apr 22, 2026Brooks Kinch, Xiaozhe Hu, Yilong Huang +6Neural Surrogate Modeling Time Series Transformers
Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA · Department of Mathematics, Tufts University, Medford, MA, USA · Department of Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway +3
Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
Apr 22, 2026Gabriel Melo, Leonardo Santiago, Peter Y. LuNeural Surrogate Modeling Chaotic Dynamical Systems
LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau · Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC · University of Campinas +1
Horizon-Constrained Rashomon Sets for Chaotic Forecasting
Apr 17, 2026Gauri Kale, Rahul Vishwakarma, Holly Diamond +2Chaotic Dynamical Systems Chaotic Time-Series Prediction
Dept. of Electrical Engineering, California State University Long Beach, USA · WorkOnward Inc., USA · Dept. of Computer Engineering & Computer Science, California State University Long Beach, USA
A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
Nov 10, 2025Xuyang Li, John Harlim, Dibyajyoti Chakraborty +1Nonlinear System Identification Neural ODEs
aSchool of Construction, University of North Carolina at Charlotte, Charlotte, 28223, NC, USA · cDepartment of Mathematics, Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, 16802, PA, USA · bCollege of Information Sciences and Technology, The Pennsylvania State University, University Park, 16802, PA, USA +1
Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data
Apr 24, 2025Davide Prosperino, Haochun Ma, Christoph RäthNonlinear System Identification Reservoir Computing
Ludwig-Maximilians-Universität München, Faculty of Physics, Geschwister-Scholl-Platz 1, 80539 Munich, Germany · Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institute for Frontier Materials on Earth and in Space, Linder Höhe, 51147 Cologne, Germany
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Jul 8, 2024Matthew J. Colbrook, Igor Mezić, Alexei StepanenkoKoopman Operator Learning Spectral Methods
DAMTP, University of Cambridge, Cambridge, CB3 0WA, UK. · University of California, Santa Barbara, CA 93106, USA.

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

Yilun Liu, Yi Zhang, Ganyu Wu, Sikuan Yan+4

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

Dynamical Systems Chaotic Dynamical Systems Chaotic Time-Series Prediction Autoregressive Modeling

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Autoregressive models are trained to predict a system's behavior one step at a time, and recursive generation allows the learned dynamics to unfold over long horizons. To what extent can such dynamics learned from local observations recover broader organization of an underlying system that was only partially observed during training? Here we study small autoregressive transformers trained from scratch on trajectories sampled from restricted parameter regimes of several non-linear dynamical systems, including logistic and sine maps, the Lorenz system, and the generalized Hopf system, with control parameters and state trajectories represented as sequences of continuous tokens. Under closed-loop evaluation at parameters far outside the training distribution, the models can recover self-similar period-doubling cascades, chaotic dynamics, and attractor structures with remarkable visual and numerical fidelity. For the logistic map, a transformer reproduces successive period doublings up to period 128, yielding a finite-order scaling ratio of 4.6687, matching the Feigenbaum constant to within

5\times10^{-4}

. We further investigate how these structures emerge over the course of training, and reveal with causal interventions how control-parameter information is processed through attention into state prediction and shapes the resulting closed-loop dynamics. These results suggest that a surprisingly narrow window into a system's local behavior may suffice for autoregressive transformers to generalize to its unseen global dynamical organization.

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