Ordinary Differential Equations

Also known as ODE

Latest papers

33 papers3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Identifying ODEs from Unstructured Data with Causal Representation Learning
Sep 29, 2026Alessandro Trenta, Riccardo Massidda, Davide Bacciu +1Causal Representation Learning Representation Identifiability
Department of Computer Science University of Pisa · Saarland Informatics Campus Saarland University & University of Amsterdam
TinyUDE: Solver-Free Universal Differential Equations on Microcontrollers via Lie-Taylor Jet Matching
Sep 22, 2026Pranavanath Balamurali, Hrishi KamireddyOn-Device Training System Identification
Department of Electrical and Computer Engineering The University of Texas at Austin · Department of Computer Science The University of Texas at Austin
Enhancing Transformer Representations of Symbolic ODE Expressions
Sep 21, 2026Xiyue Fan, Adam Prugel-Bennett, Stuart E. MiddletonTransformer Positional Encoding
University of Southampton
Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis
Sep 3, 2026Seyyed Shaho Alaviani, Yongzhi Qu, Gregory W. VoglODE Discovery Nonlinear 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
Time Without Timesteps: Simulating Coupled Dynamical Systems via Self-Consistency
Sep 3, 2026Liyu Zerihun, Mark Shinyoung LeeDynamical Systems Neural Operators
Symbolic Neural ODEs: Learning interpretable models from time-series data
Aug 22, 2026Nibodh Boddupalli, Jeff MoehlisNonlinear System Identification System Identification
Dept. of Mechanical Engineering, University of California, Santa Barbara, CA 93106
GradRepair-ODE: Certified Gradient Repair for Neural ODE Training
Aug 14, 2026Ziqian Bi, Xin Liang ChiaNeural ODEs Ordinary Differential Equations
Purdue University, West Lafayette, IN, USA · Rice University, Houston, TX, USA
Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
Aug 13, 2026Sabin Roman, Ljupco Todorovski, Saso DzeroskiSparse Identification of Nonlinear Dynamics Nonlinear System Identification
Department of Knowledge Technologies, Jožef Stefan Institute · Faculty of Mathematics and Physics, University of Ljubljana
Marrying Optimal Transport and ODEs for Unified Continuous-Time 4D Reconstruction and Tracking
Aug 10, 2026Liying Yang, Hao Mo, Jialun Liu +7Point Tracking 4D Reconstruction
SCSE, Macau University of Science and Technology · The University of Queensland · Great Bay University +3
HyperODE: Zero-Shot Surrogate for Simulation and Inference of Dynamical Systems
Aug 1, 2026Ajitesh SrivastavaNeural Surrogate Modeling Zero-Shot Learning
Northeastern University
Dynamics-aware identification of governing equations from sparse and noisy data
Jul 31, 2026Pongpisit Thanasutives, Yoshinobu KawaharaKoopman Operator Learning Sparse 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
The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recovery
Jul 20, 2026Matteo Gallo, Fabio Anselmi, Paolo LazzariScientific Discovery Parameter Identifiability
University of Trieste, Trieste, Italy · National Institute of Oceanography and Applied Geophysics - OGS, Trieste, Italy · NBFC, National Biodiversity Future Center, Palermo, Italy
RTS Smoother-Guided Learning of Physics-Based Neural Differential Models
Jul 16, 2026Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba +2Nonlinear System Identification Parameter Estimation
Department of Electrical and Computer Engineering Northeastern University · Department of Computer Science University of Massachusetts Boston · Emory University
Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System
Jul 15, 2026David Krongauz, Arad Zulti, Eran Segal +1Dynamical Systems AI 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
Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs
Jun 25, 2026Yang Pan, Helmut BölcskeiParameter Identifiability Sample Complexity
ResilPhase: Plug-and-Play Phase Mapping and Noise-Resilient Macro-Trajectory Extrapolation for Diffusion Acceleration
Jun 25, 2026Qicheng Zhao, Yu Li, Qi Sun +1Diffusion Transformer Diffusion Sampling
Zhejiang University, Hangzhou, China
Neural Architectures as Functional Priors in Physics-Informed Control Problems
Jun 11, 2026Sonia Rubio Herranz, Fernando Carlos López Hernández, Antonio López MontesDynamical Systems Ordinary Differential Equations
Department of Statistics and Operations Research (EIO), Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Software Engineering and Artificial Intelligence, Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Analysis and Applied Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain
Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds
Jun 10, 2026Ismail Huseynov, Arzu Ahmadova, Agamirza BashirovDynamical Systems Neural Network Verification
Physikalisch-Technische Bundesanstalt (PTB), Germany · Technical University of Berlin, Germany · Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany +1
PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
May 26, 2026Shailendra DabralPhysics-Informed Diffusion Models Nonlinear System Identification
Indian Institute of Technology Indore
Learning dynamical systems with biochemically informed neural ordinary differential equations
May 22, 2026Luis L. Fonseca, Reinhard C. Laubenbacher, Lucas BöttcherDynamical Systems Neural Processes
Laboratory for Systems Medicine, Department of Medicine, University of Florida, Gainesville, FL, USA · Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, Frankfurt am Main, 60322, Germany
Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics
May 21, 2026Bhaskar Ranjan Karn, Dinesh KumarODE Discovery Complex-Valued Neural Networks
Unlocking the Potential of Continual Model Merging: An ODE Perspective
May 19, 2026Lihong Lin, Haidong KangMode Connectivity Ordinary Differential Equations
Northeastern University, Shenyang, China
MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning
May 13, 2026Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood +1Neural Network Generalization System Identification
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
May 8, 2026Yuxiang Luo, Andrew PerraultNeural PDE Solvers System Identification
Department of Computer Science and Engineering The Ohio State University
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 Discovery Autonomous 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.
Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
Apr 20, 2026Abdeladhim TahimiBackpropagation Ordinary Differential Equations
Campus de Engenharias e Ciências Agrárias (CECA), Universidade Federal de Alagoas (UFAL), Rio Largo, Alagoas, 57100-000, Brazil
Neuro-Symbolic ODE Discovery with Latent Grammar Flow
Apr 17, 2026Karin Yu, Eleni Chatzi, Georgios KissasAutonomous Scientific Discovery Neurosymbolic Learning
Institute of Structural Engineering, ETH Zurich, Zurich, Switzerland · ETH AI Center, ETH Zurich, Zurich, Switzerland · Swiss Data Science Center, Zurich, Switzerland
Inverse Neural Operator for ODE Parameter Optimization
Mar 12, 2026Zhi-Song Liu, Wenqing Peng, Helmi Toropainen +5Parameter Estimation Ordinary Differential Equations
Department of Computational Engineering, Lappeenranta-Lahti University of Technology, Lahti, Finland · Atmospheric Modelling Center Lahti (AMC-Lahti), Finland · University of Helsinki, Helsinki, Finland +3
MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems
Mar 11, 2026Heikki Haario, Zhi-Song Liu, Martin Simon +1Ordinary Differential Equations Uncertainty Quantification
Lappeenranta-Lahti University of Technology LUT, Lahti, Finland · Frankfurt University of Applied Sciences, Frankfurt am Main, Germany · University of Huddersfield, Huddersfield, United Kingdom
Markovian ODE-guided scoring can assess the quality of offline reasoning traces in language models
Mar 2, 2026Arghodeep Nandi, Ojasva Saxena, Tanmoy ChakrabortyOrdinary Differential Equations Language Model Reasoning Evaluation
Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, India · Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi, New Delhi, India · Indian Institute of Technology Delhi, Abu Dhabi, UAE

Sep 29, 2026J/K move · Enter open · S save

Identifying ODEs from Unstructured Data with Causal Representation Learning

Alessandro Trenta, Riccardo Massidda, Davide Bacciu, Sara Magliacane

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

Causal Representation Learning Representation Identifiability Sparse Identification of Nonlinear Dynamics ODE Discovery Ordinary Differential Equations

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We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing methods for ODE discovery typically assume direct measurements of the variables, or do not provide theoretical guarantees on the learned variables and equations. While Causal Representation Learning (CRL) methods provide guarantees on identifying variables from high-dimensional observations up to component-wise diffeomorphisms, we show that in general these variables cannot be used directly as input to equation discovery methods, which typically assume that the variables will lead to sparse equations. So we introduce SParse Equivalent Equation Discovery AutoEncoder (SPEED-AE), a framework that combines a pretrained CRL method with a component-wise autoencoder that learns transformations of variables that are amenable to sparse ODE discovery. We show that for polynomial ODEs, this additional step allows us to restrict the identifiability of each variable from polynomial to monomial diffeomorphisms. Experiments on Lotka-Volterra, Lorenz, and a two-pendulum system show that SPEED-AE improves on the disentanglement of the CRL methods and that it recovers ODEs that are closest to the ground truth, while achieving state-of-the-art forecasting performance.