Nonlinear System Identification

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The field seeks to recover how a system changes over time from measurements, so its behavior can be explained, predicted, or controlled. Approaches include sparse equation discovery such as SINDy and symbolic regression, Koopman and kernel methods, and neural state-space or differential-equation models; many incorporate physical structure such as energy conservation or dissipation. Methods are tested on settings ranging from chaotic ODEs and oscillators to robots, vehicles, and industrial processes, often with sparse, noisy, or partially observed data. A central challenge is that good predictions on observed trajectories do not guarantee that the model is identifiable, stable over long horizons, or reliable outside the training conditions.

Latest papers

162 papers14 papers in the last four weeks, up 75% on the four weeks before. 0.1% of all new papers.

Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretability
Feb 13, 2026Ayse Tursucular, Ayush Mohanty, Nazal Mohamed +1Federated Learning Nonlinear System Identification
Georgia Institute of Technology Atlanta, GA, USA
Spatially Aware Dictionary-Free Koopman Eigenfunction Identification for Modeling and Control
Nov 27, 2025David GrasevKoopman Operator Learning Nonlinear System Identification
1*Department of Aviation Technology, University of Defence, Brno, Czech Republic.
When is a System Discoverable from Data? Discovery Requires Chaos
Nov 12, 2025Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3Dynamical Systems Nonlinear System Identification
University of Cambridge · LMU Munich and Munich Center for Machine Learning (MCML) · IBM Research
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
Neural non-canonical Hamiltonian dynamics for long-time simulations
Oct 2, 2025Clémentine Courtès, Emmanuel Franck, Michael Kraus +2Dynamical Systems Nonlinear System Identification
IRMA, MACARON · Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René Descartes 672000 Strasbourg, France. · INRIA Nancy-Grand Est, MACARON Project, Strasbourg, France. +5
Data-efficient Kernel Methods for Learning Hamiltonian Systems
Sep 21, 2025Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi +2Dynamical Systems Nonlinear System Identification
Department of Computing and Mathematical Sciences, Caltech, CA, USA. · Beyond Limits, CA, USA. · The Alan Turing Institute, London, UK. +1
Universal Learning of Nonlinear Dynamics
Aug 16, 2025Evan Dogariu, Anand Brahmbhatt, Elad HazanDynamical Systems Nonlinear System Identification
Courant Institute of Mathematical Sciences, New York University · Princeton University
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
Artifacts of Numerical Integration in Learning Dynamical Systems
Jul 19, 2025Bing-Ze Lu, Richard TsaiNumerical Integration Dynamical Systems
National Chung Cheng University, Taiwan · The University of Texas at Austin, USA
Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares
May 23, 2025Aurora Poggi, Giuseppe Alessio D'Inverno, Hjalmar Brismar +3Nonlinear System Identification Parameter Estimation
KTH Royal Institute of Technology, Department of Mathematics, Stockholm, Sweden · International School for Advanced Studies (SISSA), Trieste, Italy · KTH Royal Institute of Technology, Department of Biophysics, Stockholm, Sweden +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
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.

Feb 13, 2026J/K move · Enter open · S save

Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretability

Ayse Tursucular, Ayush Mohanty, Nazal Mohamed, Nagi Gebraeel

Georgia Institute of Technology Atlanta, GA, USA

Federated Learning Nonlinear System Identification Heterogeneous Federated Learning Root Cause Analysis Graph Attention Networks

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Networks of modern industrial systems are increasingly monitored by distributed sensors, where each system comprises multiple subsystems that generate high-dimensional time-series. These subsystems are often interdependent, making it important to understand how temporal patterns observed at one subsystem relate to those observed across others. This problem is particularly challenging in decentralized settings where raw measurements cannot be shared, and client observations are heterogeneous. Moreover, in practice, each subsystem (client) operates a fixed, proprietary model that cannot be modified or retrained, limiting the applicability of existing approaches. Separately, nonlinear dynamics make cross-client temporal interdependencies difficult to characterize, as they are embedded implicitly within nonlinear state-transition functions. This paper presents a vertical federated learning framework for learning one-step-ahead cross-client temporal interdependencies under these constraints. Each client maps high-dimensional local observations to low-dimensional latent states using a nonlinear state-space model, while a Graph Attention Network (GAT)-based central server learns a state-transition model over the communicated states. Given a candidate graph skeleton, the server learns state-dependent attention coefficients that capture cross-client interactions. We analytically relate the GAT attention coefficients to the Jacobian of the learned state-transition model, yielding a first-order characterization of cross-client interdependencies. We further establish bounded closeness of the learned dynamics and Jacobians to a corresponding centralized oracle. Synthetic experiments validate the theoretical results on controlled systems with known graph skeletons. Experiments on real-world datasets with unknown graph skeletons demonstrate superior federated root cause analysis over baselines.