ODE Discovery

ODE: Ordinary Differential Equation

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Overview

The field aims to recover the equations and parameters that generate observed trajectories, helping explain system behavior and predict beyond measured data. Common approaches include sparse regression over candidate function libraries, symbolic regression, and neural or language-model-guided search, often combined with physical constraints or domain knowledge. Methods are tested on systems such as oscillators, chaotic dynamics, biological models, and fluid flows, including settings with noise, sparse observations, or high-dimensional measurements. A central challenge is that good trajectory fits do not guarantee the correct mechanism: identifiability depends on the data and candidate model space, so reliable discovery needs structural checks and ways to quantify or resolve uncertainty.

Latest papers

CardsList

23 papers4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. LegoSR: A Unified Framework for Self-improving Agent-Guided Scientific Discovery

    Oct 24, 2026Hao Mao, Xu T. Liu, Peng Zhao +2AI Agents for Scientific DiscoverySymbolic Regression

    The Hong Kong Polytechnic University, Hong Kong SAR, China · Eastern Institute of Technology, Ningbo, China · Amazon Web Services, Seattle, USA +3

  2. Learning to Outgrow a Theory: Experimental Discovery Beyond the Initial Hypothesis Space

    Oct 6, 2026SiYuan Ma, Albert Gao, Chunzheng Zhu +6Scientific DiscoverySequential Hypothesis Testing

    Nanyang Technological University · Carnegie Mellon University · Hunan University +5

  3. APOD: reasoning-guided agentic population ordinary differential equation discovery for pharmacological digital twins

    Oct 5, 2026Romain Ferrara, Martin Soucail, Victor Gertner +7Digital TwinsLarge Language Model-Guided Scientific Discovery

    COMPutational pharmacology and clinical Oncology (COMPO), Inria Center at University Côte d’Azur, Cancer Research Center of Marseille, Marseille, France · Department of Nuclear Medicine, Institut Paoli-Calmettes, ENETS Center of Excellence, IPC NET Center, Marseille, France · Centre for Computational Biology (CBIO), Mines Paris, PSL University, Paris, France +3

  4. Identifying ODEs from Unstructured Data with Causal Representation Learning

    Sep 29, 2026Alessandro Trenta, Riccardo Massidda, Davide Bacciu +1Causal Representation LearningRepresentation Identifiability

    Department of Computer Science University of Pisa · Saarland Informatics Campus Saarland University & University of Amsterdam

  5. FluxDisco: Symbolic Regression for Stoichiometric Dynamical Systems via Monte Carlo Graph Search

    Sep 4, 2026Cassandra Durr, Alvaro Köhn-Luque, Chris Jewell +1ODE DiscoverySymbolic Regression

    Lancaster University · University of Oslo

  6. Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis

    Sep 3, 2026Seyyed Shaho Alaviani, Yongzhi Qu, Gregory W. VoglODE DiscoveryNonlinear System Identification

    Department of Mechanical Engineering University of Minnesota-Twin Cities Minneapolis, MN 55455, USA · Department of Mechanical Engineering University of Utah Salt Lake City, UT 84112, USA · National Institute of Standards and Technology Gaithersburg, MD 20899, USA

  7. Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration

    Aug 13, 2026Sabin Roman, Ljupco Todorovski, Saso DzeroskiSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Department of Knowledge Technologies, Jožef Stefan Institute · Faculty of Mathematics and Physics, University of Ljubljana

  8. Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers

    Aug 1, 2026Farbod Faraji, Francesco BelardinelliNonlinear System IdentificationAutonomous Scientific Discovery

    Department of Computing, Huxley Building, Imperial College London 180 Queen’s Gate, South Kensington, London SW7 2RH, United Kingdom

  9. Dynamics-aware identification of governing equations from sparse and noisy data

    Jul 31, 2026Pongpisit Thanasutives, Yoshinobu KawaharaKoopman Operator LearningSparse Identification of Nonlinear Dynamics

    Center for Advanced Intelligence Project (AIP), RIKEN, Osaka, Japan · 2Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan

  10. The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recovery

    Jul 20, 2026Matteo Gallo, Fabio Anselmi, Paolo LazzariScientific DiscoveryParameter Identifiability

    University of Trieste, Trieste, Italy · National Institute of Oceanography and Applied Geophysics - OGS, Trieste, Italy · NBFC, National Biodiversity Future Center, Palermo, Italy

  11. Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System

    Jul 15, 2026David Krongauz, Arad Zulti, Eran Segal +1Dynamical SystemsAI Agents for Scientific Discovery

    Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel · Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates +2

  12. LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data

    Jul 1, 2026Hanning Yang, Meropi Karakioulaki, Lennart Purucker +3Autonomous Scientific DiscoveryLarge Language Model-Guided Scientific Discovery

    Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Germany · Department of Dermatology, Medical Faculty and Medical Center, University of Freiburg, Germany · Prior Labs, University of Freiburg, Germany

  13. Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs

    Jun 25, 2026Yang Pan, Helmut BölcskeiParameter IdentifiabilitySample Complexity

  14. LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search

    Jun 23, 2026Nikhil Abhyankar, Sha Li, Sanchit Kabra +3Nonlinear System IdentificationSystem Identification

    Virginia Tech

  15. Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions

    May 27, 2026Yuanyuan Wang, Wenjie Wang, Kun Zhang +1Parameter IdentifiabilityLatent Dynamics Modeling

    Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · University of Melbourne, Melbourne, Australia · Carnegie Mellon University, Pittsburgh, USA

  16. Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

    May 21, 2026Bhaskar Ranjan Karn, Dinesh KumarODE DiscoveryComplex-Valued Neural Networks

  17. Discovery of Nonlinear Dynamics with Automated Basis Function Generation

    May 10, 2026Mohammad Amin Basiri, Charles NicholsonSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Data Science and Analytics Institute, University of Oklahoma, Norman, OK, USA · School of Industrial and Systems Engineering, University of Oklahoma, Norman, OK, USA

  18. Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation

    May 8, 2026Sum Kyun Song, Bong Gyun Shin, Jae Yong LeeAI Agents for Scientific DiscoveryAutonomous Scientific Discovery

    Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea · Department of AI Big Data, Daejin University, Pocheon-si, Republic of Korea.

  19. PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability

    May 7, 2026Federico J. GonzalezAutonomous Scientific DiscoveryInverse Problems

    Physics Institute of Rosario (IFIR), CONICET-UNR, Blvd. 27 de Febrero 210 Bis, Rosario, S2000EZP, Argentina.

  20. Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

    Apr 22, 2026Zhiheng Chen, Urban Fasel, Anastasia BizyaevaSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 14850 · Department of Aeronautics, Imperial College London, London, United Kingdom

  21. Neuro-Symbolic ODE Discovery with Latent Grammar Flow

    Apr 17, 2026Karin Yu, Eleni Chatzi, Georgios KissasAutonomous Scientific DiscoveryNeurosymbolic Learning

    Institute of Structural Engineering, ETH Zurich, Zurich, Switzerland · ETH AI Center, ETH Zurich, Zurich, Switzerland · Swiss Data Science Center, Zurich, Switzerland

  22. LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models

    Mar 21, 2026Amirmohammad Ziaei Bideh, Jonathan GryakODE DiscoveryDynamical Systems

    The Graduate Center, CUNY New York, New York, USA · Queens College and The Graduate Center, CUNY New York, New York, USA

  23. Symmetry-Constrained Language-Guided Program Synthesis for Discovering Governing Equations from Noisy and Partial Observations

    Mar 6, 2026Mirza Samad Ahmed Baig, Syeda Anshrah GillaniODE DiscoveryAutonomous Scientific Discovery

    Fandaqah (Owned by Dyafa), Al Khobar, Eastern Province, Saudi Arabia · Hamdard University, Karachi, Pakistan