Control for Deep and Federated Learning

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Machine Learning and Control: Foundations, Advances, and Perspectives

Author(s): Enrique Zuazua
Published in: Proceedings of the International Congress of Mathematicians 2026 - Volume 7: Invited Lectures (Sections 15–20), 2026
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/ARXIV.2510.03303

Shape and Topology Optimization for Network of Timoshenko Beams

Author(s): Meizhi Qian, Jan Sokołowski
Published in: 2025 29th International Conference on Methods and Models in Automation and Robotics (MMAR), 2025
Publisher: IEEE
DOI: 10.1109/MMAR65820.2025.11150880

Moments, time-inversion and source identification for the heat equation

Author(s): Kang Liu, Enrique Zuazua
Published in: Inverse Problems, Issue 42, 2026, ISSN 0266-5611
Publisher: IOP Publishing
DOI: 10.1088/1361-6420/AE3797

Representation and regression problems in neural networks: Relaxation, generalization, and numerics

Author(s): Kang Liu, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, Issue 35, 2025, ISSN 0218-2025
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218202525500228

Nonlinear equilibrium transitions in a potential game model for federated learning

Author(s): Kang Liu, Ziqi Wang, Enrique Zuazua
Published in: Physica D: Nonlinear Phenomena, Issue 495, 2026, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/J.PHYSD.2026.135288

On control networks over finite lattices

Author(s): Zhengping Ji, Daizhan Cheng
Published in: Science China Information Sciences, Issue 68, 2025, ISSN 1674-733X
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S11432-024-4252-7

Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications

Author(s): Ziqian Li, Kang Liu, Lorenzo Liverani, Enrique Zuazua
Published in: SIAM Journal on Numerical Analysis, Issue 64, 2026, ISSN 0036-1429
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1679690

Approximate and Weighted Data Reconstruction Attack in Federated Learning

Author(s): Yongcun Song, Ziqi Wang, Enrique Zuazua
Published in: IEEE Transactions on Big Data, Issue 12, 2026, ISSN 2332-7790
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.48550/ARXIV.2308.06822

Random batch methods for discretized PDEs on graphs

Author(s): Martin Hernandez, Enrique Zuazua
Published in: Journal of Computational Physics, Issue 569, 2026, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.48550/ARXIV.2506.11809

Tracking Controllability for Finite-Dimensional Linear Systems

Author(s): Sebastian Zamorano, Enrique Zuazua
Published in: IEEE Transactions on Automatic Control, 2026, ISSN 0018-9286
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.48550/ARXIV.2407.18641

Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach

Author(s): Timothée Crin-Barat, Lorenzo Liverani, Ling-Yun Shou, Enrique Zuazua
Published in: Journal de Mathématiques Pures et Appliquées, Issue 202, 2025, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/J.MATPUR.2025.103757

Regional and partial observability and control of waves

Author(s): Belhassen Dehman, Sylvain Ervedoza, Enrique Zuazua
Published in: Comptes Rendus. Mathématique, Issue 363, 2025, ISSN 1631-073X
Publisher: MathDoc/Centre Mersenne
DOI: 10.5802/CRMATH.805

Invariant and Dual-Invariant Subspaces of k-Valued Networks

Author(s): Daizhan Cheng, Hongsheng Qi, Xiao Zhang, Zhengping Ji
Published in: Journal of Systems Science and Complexity, Issue 38, 2025, ISSN 1009-6124
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S11424-025-4411-1

"Optimal <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" altimg=""si17.svg"" display=""inline"" id=""d1e336""><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-approximation of convex sets by convex subsets"

Author(s): Zakaria Fattah, Ilias Ftouhi, Enrique Zuazua
Published in: Nonlinear Analysis, Issue 261, 2025, ISSN 0362-546X
Publisher: Elsevier BV
DOI: 10.1016/J.NA.2025.113866

Clustering in Pure-Attention Hardmax Transformers and Its Role in Sentiment Analysis

Author(s): Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
Published in: SIAM Journal on Mathematics of Data Science, Issue 7, 2026, ISSN 2577-0187
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M167086X

Cluster-Based Classification with Neural ODEs via Control

Author(s): Antonio Álvarez-Lόpez, Rafael Orive-Illera, Enrique Zuazua
Published in: Journal of Machine Learning, Issue 4, 2026, ISSN 2790-203X
Publisher: Global Science Press
DOI: 10.4208/JML.241114

Observer-Based Realization of Control Systems

Author(s): Daizhan Cheng, Xiao Zhang, Zhengping Ji, Changxi Li
Published in: IEEE Transactions on Automatic Control, Issue 71, 2026, ISSN 0018-9286
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/TAC.2025.3604656

Exact sequence interpolation with transformers

Author(s): Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
Published in: Mathematical Foundations of Machine Learning, Issue 2, 2026, ISSN 3059-3492
Publisher: Springer Science and Business Media LLC
DOI: 10.48550/ARXIV.2502.02270

Pointwise constraints for scalar conservation laws with positive wave velocity

Author(s): Nicola De Nitti, Denis Serre, Enrique Zuazua
Published in: Zeitschrift für angewandte Mathematik und Physik, Issue 76, 2025, ISSN 0044-2275
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00033-025-02459-0

Topological Derivative Method for Design and Control of Timoshenko Beam Networks

Author(s): Meizhi Qian, Jairo Rocha de Faria, Antonio J. B. Santos, Jan Sokołowski, Ana P. P. Wyse
Published in: Applied Mathematics & Optimization, Issue 93, 2026, ISSN 0095-4616
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00245-025-10369-W

Sharp numerical approximation of the Hardy constant

Author(s): Liviu I. Ignat, Enrique Zuazua
Published in: Discrete and Continuous Dynamical Systems, Issue 54, 2026, ISSN 1078-0947
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/DCDS.2025165

FedADMM-InSa: An inexact and self-adaptive ADMM for federated learning

Author(s): Yongcun Song, Ziqi Wang, Enrique Zuazua
Published in: Neural Networks, Issue 181, 2025, ISSN 0893-6080
Publisher: Elsevier BV
DOI: 10.1016/J.NEUNET.2024.106772

Boundary sidewise observability of the wave equation

Author(s): Belhassen Dehman, Enrique Zuazua
Published in: Journal of the European Mathematical Society, 2026, ISSN 1435-9855
Publisher: European Mathematical Society - EMS - Publishing House GmbH
DOI: 10.4171/JEMS/1688

On universal eigenvalues and eigenvectors of hypermatrices

Author(s): Daizhan Cheng, Zhengping Ji
Published in: Journal of the Franklin Institute, Issue 362, 2025, ISSN 0016-0032
Publisher: Elsevier BV
DOI: 10.1016/J.JFRANKLIN.2025.108126

Deep neural ODE operator networks for PDEs

Author(s): Ziqian Li, Kang Liu, Yongcun Song, Hangrui Yue, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, Issue 36, 2026, ISSN 0218-2025
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218202526420054

Control of hyperbolic and parabolic equations on networks and singular limits

Author(s): Jon Asier Bárcena-Petisco, Márcio Cavalcante, Giuseppe Maria Coclite, Nicola De Nitti, Enrique Zuazua
Published in: Mathematical Control and Related Fields, Issue 15, 2025, ISSN 2156-8472
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/MCRF.2024015

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