Neural ODEs

ODE: Ordinary Differential Equation

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Overview

Neural ODEs represent hidden states or physical systems as evolving continuously according to a learned vector field, with numerical solvers used to compute their trajectories. Researchers use them for irregular time-series forecasting, scientific simulation, control, and generative modeling, often combining them with controlled or stochastic dynamics, graph networks, or known physical laws. Common approaches include hybrid mechanistic-neural models, physics-informed constraints, and structure-preserving methods such as Hamiltonian or symplectic models; evaluations span dynamical-system benchmarks, irregular clinical data, and engineering simulations. A central tension is balancing flexible learned dynamics with physical consistency and long-horizon reliability, while managing solver cost, stiffness, noisy observations, and sensitivity to numerical error.

Latest papers

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91 papers7 papers in the last four weeks, up 40% on the four weeks before. 0.0% of all new papers.

  1. Data-driven Discovery of Lie Symmetries and First Integrals with Latent ODEs

    Oct 25, 2026Matt L. Wiemman, Peter MelchiorSymmetry DiscoveryLie Group Methods

    Princeton University

  2. Dynamic System Inspired Continuous Large Language Model for AI4Science Tasks

    Oct 18, 2026Zhaoxin Fan, Zheng Zhu, Yuqing Ma +3Neural ODEsScientific Reasoning in Language Models

    Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, 100191, Beijing, China. · School of Artificial Intelligence, Beihang University, Beijing, 100191, Beijing, China. · GigaAI, Beijing, 100191, Beijing, China.

  3. Learning and Forecasting Multiscale Spatiotemporal Epidemic Dynamics with Lagrangian-Eulerian Graph Neural ODEs

    Oct 15, 2026Jinyi Duan, Qian Li, Biao TangEpidemic ForecastingSpatial Epidemic Modeling

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China . · School of Mathematics and Statistics, Xi’an University of Technology, Xi’an, 710054, People’s Republic of China . · Center for Intersection of Mathematics and Life Sciences, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China .

  4. CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting

    Oct 14, 2026Chengyi Pan, Huangqimei Zheng, Hao XueTime Series ModelingExogenous Time Series Forecasting

    UGOD, HKUST-GZ · School of Software, Yunnan University · UGOD, The Hong Kong University of Science and Technology (Guangzhou)

  5. Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing

    Oct 10, 2026Pooja Algikar, Stefano Fenu, Kumarsinh Jhala +1Multimodal Sensor FusionNeural ODEs

    Argonne National Laboratory, Lemont, Illinois, USA

  6. Continuous-Time Cloth Dynamics with Physics-Informed Neural ODEs

    Oct 9, 2026Yingdong Ru, Lipeng Zhuang, Zhuo He +1Deformable Object SimulationPhysics-Informed ML

    University of Glasgow, Glasgow, United Kingdom

  7. Safe-by-Design Learning via Energy-based Neural Networks

    Sep 29, 2026Simone Betteti, Morteza Lahijanian, Luca LaurentiSafety-Critical ControlControl Barrier Functions

    RIAS Lab The Italian Institute of Artificial Intelligence for Industry Torino, 10129, ITA · RECUV University of Colorado Boulder Boulder, CO 80303, USA · Delft Center for Systems and Control, TU Delft, Delft, 2600 AA, The Netherlands

  8. DevelopmentODE: Structured Neural ODEs for Early Brain Development Dynamics Across a Decade

    Sep 27, 2026Kaiqiao Han, Haitao Chen, Bryan Quah +5Trajectory PredictionNeural ODEs

    University of California, Los Angeles · Cedars-Sinai Medical Center · Emory University +1

  9. Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees

    Sep 26, 2026Omkar Sudhir PatilNeural ODEsNeural Network Training Dynamics

    Division of Electrical and Computer Engineering Louisiana State University Baton Rouge, LA 70803, USA

  10. Continuous-Time Machine Learning: A Unified Mathematical Perspective

    Sep 15, 2026Waleed Razzaq, Yun-Sheng Zhao, Yun-Bo ZhaoDynamical SystemsNeural ODEs

    School of Automation University of Science and Technology of China Hefei, Anhui

  11. Continuous Learning of Gravity Field Irregularities Around Small Bodies via Neural Hamiltonian ODEs

    Sep 10, 2026Giacomo Acciarini, Dario IzzoDynamical SystemsHamiltonian Neural Networks

    Advanced Concepts Team, European Space Agency, ESTEC, Noordwijk, The Netherlands

  12. An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamics

    Sep 3, 2026Sebastian Schaffer, Lukas ExlLatent Dynamics ModelingEnergy-Based Models

    Math. AI/ML, Wolfgang Pauli Institute, Vienna, Austria · Department of Mathematics, University of Vienna, Vienna, Austria

  13. Learning Reduced-Order Dynamics with Singularity via Latent-Augmented Neural Ordinary Differential Equations

    Aug 22, 2026Xiaorui Wang, Yu Zhou, Wenjie Mei +3Reduced-Order ModelingNeural ODEs

    Lanzhou University of Technology, School of Automation and Electrical Engineering, Lanzhou, 730050, Gansu, China · Hiroshima University, Graduate School of Advanced Science and Engineering, Higashihiroshima, 739-0046, Hiroshima, Japan · Nanjing University - Suzhou Campus, School of Robotics and Automation, Suzhou, 215163, Jiangsu, China +1

  14. Symbolic Neural ODEs: Learning interpretable models from time-series data

    Aug 22, 2026Nibodh Boddupalli, Jeff MoehlisNonlinear System IdentificationSystem Identification

    Dept. of Mechanical Engineering, University of California, Santa Barbara, CA 93106

  15. GradRepair-ODE: Certified Gradient Repair for Neural ODE Training

    Aug 14, 2026Ziqian Bi, Xin Liang ChiaNeural ODEsOrdinary Differential Equations

    Purdue University, West Lafayette, IN, USA · Rice University, Houston, TX, USA

  16. Virtual Temperature Sensors in Power Transformers Using Neural Ordinary Differential Equations

    Aug 13, 2026Berk Hadzhamolla, Alexander Johannes Stasik, Signe Riemer-SørensenPhysics-Informed MLNeural ODEs

    University of Oslo, Oslo, 0316, Norway · 2,3 SINTEF AS, Department of Mathematics and Cybernetics, Oslo, Norway · Department of Data Science, Norwegian University of Life Sciences, ˚As, Norway

  17. Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies

    Aug 11, 2026Ziqian Li, Nikolaos M. MatzakosDynamical SystemsNeural ODEs

    Chair for Dynamics, Control, Machine Learning and Numerics, Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany · School of Pedagogical & Technological Education (ASPETE), Marousi Attikis, 151 22 Athens, Greece

  18. Flowing Through States: Neural ODE Regularization for Reinforcement Learning

    Aug 6, 2026Mohamed Ghanem, Bernd FinkbeinerLatent Dynamics ModelingRepresentation Learning for RL

    CISPA Helmholtz Center for Information Security · Technical University of Munich

  19. Training Crossroads for Recurrent Vision Transformers: Recurrence, Neural ODEs, and Deep Supervision

    Aug 5, 2026Grzegorz Gruszczynski, Pawel Olszowiec, Michal Byra +2Recurrent TransformersNeural ODEs

    Samsung AI Center, Warsaw, Poland · Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

  20. Operator Neural Jump ODEs: L2L^2-optimal prediction in function spaces

    Jul 25, 2026Florian Krach, Oliver Löthgren, Josef TeichmannTime Series ForecastingNeural Network Approximation Theory

    Department of Mathematics ETH Zurich

  21. Multiplicity of Stable Attractors in Disordered Neural Models

    Jul 24, 2026Raffaele Marino, Roberto Livi, Antonio PolitiDynamical SystemsLarge Deviation Principles

    Butterfly Decisions srl, Via dei Principati 74 - 84122 Salerno, Italy · University of Florence, Department of Physics and Astronomy, Via G. Sansone 1 - 50019 Sesto Fiorentino (FI), Italy and Istituto dei Sistemi Complessi, CNR, Via Madonna del Piano 10 – 50019 Sesto Fiorentino (FI), Italy · Istituto dei Sistemi Complessi, CNR, Via Madonna del Piano 10 – 50019 Sesto Fiorentino (FI), Italy and Institute of Pure and Applied Mathematics, Department of Physics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

  22. ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs

    Jul 22, 2026Yordanka Velikova, Mahdi Saleh, Liming Kuang +1Neural ODEsDeformable Object Simulation

    Technical University of Munich · Munich Center for Machine Learning (MCML)

  23. FlowSonic: Stable Zero-Shot Music Editing via High-Order Trajectory Integration

    Jul 20, 2026Ali Boudaghi, Hadi ZareDiffusion Model InversionDiffusion Transformer

  24. Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls

    Jul 17, 2026Henrik Lange, Reik Thormann, Philipp BekemeyerGraph Neural NetworksPDE Surrogate Modeling

    German Aerospace Center (DLR), Lilienthalpl. 7, 38108 Brunswick, Germany · Airbus Operations, Airbus Allee 1, 28199 Bremen, Germany

  25. Spatial Transport of Integration Error in Generative ODEs

    Jul 17, 2026Songheng YinDiffusion Model SamplingFew-Step Diffusion Sampling

    Columbia University

  26. RTS Smoother-Guided Learning of Physics-Based Neural Differential Models

    Jul 16, 2026Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba +2Nonlinear System IdentificationParameter Estimation

    Department of Electrical and Computer Engineering Northeastern University · Department of Computer Science University of Massachusetts Boston · Emory University

  27. Advances in Neural Controlled Differential Equations

    Jul 6, 2026Benjamin WalkerNeural Controlled Differential EquationsNeural ODEs

    Balliol College, University of Oxford

  28. ENC-ODE: Event-level Neurodegenerative Modeling in Continuous Time with Neural ODEs

    Jun 29, 2026Yujee Song, Seunghun Baek, Guorong Wu +1Latent Dynamics ModelingLongitudinal EHR Modeling

    Pohang University of Science and Technology, Pohang, South Korea · University of North Carolina at Chapel Hill, Chapel Hill, USA

  29. RainODE: Continuous-Time Precipitation Forecasting with Latent Neural ODEs

    Jun 29, 2026Yeeun Seong, Doyi Kim, Minseok Seo +1Precipitation ForecastingTime Series Forecasting

    Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea

  30. Symplectic Neural Networks for learning Generalized Hamiltonians

    Jun 25, 2026Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta +2Dynamical SystemsSymplectic RNNs

    Computer Science Department, Indraprasth Institute of Information Technology, New Delhi, India 110020 · Athena Research and Innovation Center, Marousi, Greece 15125 · HSBC Holdings, Singapore