System Identification

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System identification uses observations of a system, often alongside controlled inputs, to infer how it changes over time and how it will respond to new conditions. Approaches range from ARX and state-space or subspace methods to sparse equation discovery with SINDy, Koopman operators, neural ODEs, and physics-structured models such as Hamiltonian networks; Bayesian and active-learning methods help choose experiments and quantify uncertainty. These tools support prediction and control in settings including robotics, industrial processes, physical experiments, and systems observed through video. A central challenge is that accurate prediction on observed data does not guarantee that the underlying laws or parameters are identifiable, especially with sparse, noisy, partial, or weakly excited observations.

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157 papers19 papers in the last four weeks, down 10% on the four weeks before. 0.1% of all new papers.

Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems
Jul 26, 2025Jiaqiang Li, Jianbin Tan, Xueqin WangSystem Identification Nonlinear System Identification
School of Management, University of Science and Technology of China, Anhui, Hefei, China · Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA
Learning thermodynamic master equations for open quantum systems
Jun 2, 2025Peter Sentz, Stanley Nicholson, Yujin Cho +3Quantum System Identification Interpretable ML
Department of Data and Decision Sciences, Emory University, Atlanta, GA 30322 · 2Division of Applied Mathematics, Brown University, Providence, RI 02912 · 3Lawrence Livermore National Laboratory, Livermore, CA 94550
Manifold meta-learning for reduced-complexity neural system identification
Apr 16, 2025Marco Forgione, Ankush Chakrabarty, Dario Piga +2System Identification Meta-Learning
SUPSI, IDSIA - Dalle Molle Institute for Artificial Intelligence, Lugano, Switzerland. · Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA, USA. · IMT School for Advanced Studies Lucca, Lucca, Italy.
Automated Discovery of Operable Dynamics from Videos
Oct 14, 2024Kuang Huang, Dong Heon Cho, Boyuan ChenDynamical Systems Latent Dynamics Modeling
Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, New York, 10027, NY, USA. · Department of Computer Science, Duke University, 308 Research Dr., Durham, 27705, NC, USA. · Department of Mechanical Engineering and Material Science, Duke University, 121 Hudson Hall, Durham, 27708, NC, USA. +1
Nonparametric Control Koopman Operators
May 12, 2024Petar Bevanda, Bas Driessen, Lucian Cristian Iacob +3Koopman Operator Learning System Identification
Chair of Information-oriented Control, TU München, Germany · Control Systems Group, TU/e, Eindhoven, The Netherlands · Systems and Control Laboratory, HUNREN Institute for Computer Science and Control, Budapest, Hungary +2
Inferring Inference
Oct 4, 2023Rajkumar Vasudeva Raju, Zhe Li, Scott Linderman +1Neural Algorithmic Reasoning System Identification
Department of ECE, Rice University · Department of Neuroscience, Baylor College of Medicine · Department of Statistics, Stanford University +3
From system models to class models: An in-context learning paradigm
Aug 25, 2023Marco Forgione, Filippo Pura, Dario PigaMeta-Learning In-Context Learning
IDSIA Dalle Molle Institute for Artificial Intelligence USI-SUPSI, Via la Santa 1, CH-6962 Lugano-Viganello, Switzerland.

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Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems

Jiaqiang Li, Jianbin Tan, Xueqin Wang

School of Management, University of Science and Technology of China, Anhui, Hefei, China · Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA

System Identification Nonlinear System Identification Autonomous Scientific Discovery

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Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical simulation. However, many existing approaches rely on accurate derivative estimation and are limited to first-order dynamical systems, restricting their applicability in real-world scenarios. In this work, we propose Sparse Equation Matching (SEM), a unified framework that encompasses several existing equation discovery methods under a common formulation. SEM introduces an integral-based sparse regression approach using Green's functions, enabling derivative-free estimation of differential operators and their associated driving functions in general-order dynamical systems. The effectiveness of SEM is demonstrated through extensive simulations, benchmarking its performance against derivative-based approaches. We then apply SEM to electroencephalographic (EEG) data recorded during multiple oculomotor tasks, collected from 52 participants in a brain-computer interface experiment. Our method identifies active brain regions across participants and reveals task-specific connectivity patterns. These findings offer valuable insights into brain connectivity and the underlying neural mechanisms.