Project name: DASEL, Ciencia de Datos para Redes Eléctricas
Project reference: TED2021-131390B-I00
AEI: TED2021-131390B-I00/ AEI/10.13039/501100011033 DASEL
Funding source: MINECO. Ministry of Science, Innovation and Universities. Proyectos de Transición Ecológica y Transición Digital 2021
Duration: December 2022 – September 2025
Principal Investigator (PI): Enrique Zuazua, Umberto Biccari
About the Project
Digital technologies have become an important part of our daily routine, impacting the way we interact with people and do business. A more productive and environmentally friendly economy requires a methodical research and innovation strategy and implementation with an integrated vision of the future. However, to fully embrace and enhance the many benefits of this technological revolution, it is critical to address the challenges it poses by creating policies and implementing new solutions that give society the confidence, skills and resources it needs to digitize and grow. Data science and machine learning are players in this technological innovation. Today, companies and organizations have become aware of the importance of using these tools to transform data into a competitive advantage by redefining their products and services.
In recent years, data science has become a priority for our society, as well as for companies, which are investing heavily in this sector. At the basis of any technological innovation is a deep and complete understanding of the fundamental principles that govern it. While data science and machine learning are basically present today in any kind of industrial and technological applications, many constituent aspects of these disciplines are still only partially understood. This has opened a new and very fertile field of research for applied mathematicians who, in recent years, have widely exploited this possibility to develop new branches of pure and applied innovative research. Under this perspective, this project aims to contribute to the green and digital transition by addressing some specific issues in data science and machine learning from the point of view of applied mathematics in the field of energy. On the one hand, we will consider key constitutive aspects of these fields in order to strengthen their mathematical foundations. On the other hand, we will consider practical applications in selected but very relevant problems in fields such as electrical engineering and electrical network design. These applications, related to the integration of distributed generation systems from renewable sources such as photovoltaic, wind or hydroelectric power, represent a priority strategic objective for a more sustainable society of the future.
Summary
Digital technologies are reshaping interactions and business operations, driving the need for a greener strategic approach to research and innovation for more productive economy. To fully leverage the benefits of this technological revolution, it is crucial to address the challenges it poses by creating policies and implementing new solutions that equip society with the confidence, skills, and resources needed for digital growth. Data Science and Machine Learning are the core of this transformation helping organizations gain a competitive edge by redefining products and services as a timely investment for our society and for business and industry. This has opened up a very fertile field of research for applied mathematicians, leading to make new advancements in both pure and applied research strengthening mathematical foundations and practical applications to selected but very relevant problems in areas such as electrical engineering and electrical network design balancing technoligical progress with preparing society for improved sustainability.
Publications
• Li Z., Liu K., Song Y., Yue H. & Zuazua E. (2025) Deep Neural ODE Operator Networks for PDEs, arXiv:2510.15651
• Affili E. & Zuazua E. (2025) Controllability of diffusive Lotka – Volterra strongly competitive systems under boundary constrained controls, arXiv: 2508.00713
• Alcalde A., Fantuzzi G. & Zuazua E. (2025) Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis, SIAM J. Math. Data Sci., SIMODS, 7(3), 1367–1393. https://doi.org/10.1137/24M167086X, arxiv: 2407.01602
• Alcalde A., Fantuzzi G. & Zuazua E. (2025) Exact Sequence Classification with Hardmax Transformers, arxiv:2502.02270
• Biccari U. (2025) Spiking Neural Networks: a theoretical framework for Universal Approximation and training, arxiv:2509.21920
• Lyu K., Biccari U. & Wang J. (2025) Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels, arxiv:2508.03242
• Morales R. & Biccari U. (2025) A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints, arxiv:2507.13983
• Biccari U. , Warma M. & Zuazua E. (2025) Boundary observation and control for fractional heat and wave equations, arXiv: 2504.17413
• Biccari U. & Zuazua E. (2025) Gaussian Beam ansatz for finite difference wave equations, FoCM, 25(1), pp. 1–54, https://doi.org/10.1007/s10208-023-09632-9
• Bárcena-Petisco J.A., Cavalcante M., Coclite G.M., De Nitti N. & Zuazua E. (2025) Control of Hyperbolic and Parabolic Equations on Networks and Singular limits, MCRF, 15(1), p. 348-389, https://doi.org/10.3934/mcrf.2024015
• Crin-Barat T., Liverani L., Shou L.Y. & Zuazua E. (2025) Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach, J. Math. Pures Appl., 202, p. 103757, https://doi.org/10.1016/j.matpur.2025.103757
• De Nitti N., Serre D. & Zuazua E. (2025) Pointwise constraints for scalar conservation laws with positive wave velocity, Z. Angew. Math. Phys., 76(111), https://doi.org/10.1007/s00033-025-02459-0
• Dehman B., Ervedoza S. & Zuazua E. (2025) Regional and partial observability and control of waves. Special issue on the memory of H. Brezis. C. R. Acad. Sci. Paris. arXiv: 2504.18976
• Dehman B. & Zuazua E. (2025) Boundary sidewise observability of the wave equation. J. Eur. Math. Soc. (JEMS), arXiv: 2310.19456, https://doi.org/10.4171/jems/1688
• Fattah Z., Ftouhi I. & Zuazua E. (2025) Optimal Lp-approximation of convex sets by convex subsets, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 261(18), https://doi.org/10.1016/j.na.2025.113866
• Fernandes Barreira J., Sônego M. & Zuazua E. (2025) Boundary and Interior Control in a Diffusive Lotka-Volterra Model, arxiv:2511.01453
• Ftouhi I. & Zuazua E. (2025) Sensor placement via large deviations in the eikonal equation, arXiv: 2508.21469
• Hernández M. & Zuazua E. (2025) Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks, arxiv:2409.06555
• Ignat L.I. & Zuazua E. (2025) Optimal convergence rates for the finite element approximation of the Sobolev constant, arXiv: 2504.09637
• Ignat L.I. & Zuazua E. (2025) Sharp Numerical Approximation of the Hardy Constant: Discrete Contin. Dyn. Syst., https://doi.org/10.3934/dcds.2025165
• Li Z., Liu K., Liverani L. & Zuazua E. (2025) Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications, arXiv: 2407.17092
• Liu K. & Zuazua E. (2025) A PDE perspective on generative diffusion models, arxiv:2511.05940
• Liu K. & Zuazua E. (2025) Moments, time-inversion and source identification for the heat equation, arXiv: 2507.02677
• Liu K. & E. Zuazua E. (2025) Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics, Math. Models Methods Appl. Sci., 35(6), 1471-1521, https://doi.org/10.1142/S0218202525500228
• Liverani L., Steynberg M. & Zuazua E. (2025) HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling, arXiv: 2509.14123
• Song Y., Wang Z. & Zuazua E. (2025) FedADMM-InSa: An inexact and self-adaptive ADMM for federated learning, Neural Networks, 181, 106-772, https://doi.org/10.1016/j.neunet.2024.106772
• Sônego M. & Zuazua E. (2025) Control of a Lotka-Volterra System with Weak Competition, Communications in Information and Systems (CIS), arXiv: 2409.20279, preprint, accepted.
• Trélat E. & E. Zuazua E. (2025) Turnpike in optimal control and beyond: A survey, Modeling and Optimization in Space Engineering. Challenges of the Future. arXiv: 2503.20342, preprint, accepted.
• Veldman D., Borkowski A. & Zuazua E. (2025) Stability and Convergence of a Randomized Model Predictive Control Strategy, IEEE Trans. Autom. Control, 69(9), 6253-6260. https://doi.org/10.1109/TAC.2024.3375253
• Zuazua E. (2025) Machine Learning and Control: Foundations, Advances, and Perspectives (Conference contribution, submitted), arXiv: 2510.03303
• Álvarez López A., Orive-Illera R., Zuazua E. (2025) Cluster-based classification with neural ODEs via control, J. Mach. Learn., 4(2), 128-156. https://doi.org/10.4208/jml.241114
• Alvarez-Lopez A., Rafael OI. & Zuazua E. (2024) Optimized classification with neural ODEs via separability, https://doi.org/10.48550/arXiv.2312.13807
• Coclite G.M., De Nitti N., Maddalena F., Orlando D. & Zuazua E. (2024) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings. Math. Models Methods Appl. Sci., 34(8), 1445–1482. https://doi.org/10.1142/S021820252450026X
• Ftouhi I. & Zuazua E. (2024) Optimal Placement and Shape Design of Sensors via Geometric Criteria. European Control Conference, ECC 2024 (Stockholm, SWE, June 25-28, 2024)
• Hernández, M. & Zuazua, E. (2024). Uniform turnpike property and singular limits. Acta Appl. Math., 190, 33. https://doi.org/10.1007/s10440-024-00640-7
• Lazar, M. & Zuazua, E. (2024). Eigenvalue bounds for the Gramian operator of the heat equation. Automatica, 164, 11. https://doi.org/10.1016/j.automatica.2024.111653
• Lecaros, R., López-Ríos, J., Montecinos, G. I., & Zuazua, E. (2024). Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements. Math. Methods Appl. Sci., 47(18), 13973–14004. https://doi.org/10.1002/mma.10251
• Bazarra N., Fernández J.R., Liverani L., Quintanilla R. (2024) Analysis of a thermoelastic problem with the Moore–Gibson–Thompson microtemperatures. J. Comput. Appl. Math., 438(115571), https://doi.org/10.1016/j.cam.2023.115571
• Ruiz-Balet, D. & Zuazua, E. (2024). Pattern control via Diffussion interaction, arXiv: 2407.17514
• Zamorano, S. & Zuazua, E. (2024). Tracking controllability for finite-dimensional linear systems, arXiv: 2407.18641
• Zuazua E. (2024) Fourier series and sidewise profile control of 1-d waves, Documents Mathématiques of the French Mathematical Society (SMF). In honor of Yves Meyer, 22, arXiv: 2308.04906
• Zuazua E. (2024) Progress and future directions in machine learning through control theory. FGS2024. French-German-Spanish Conference on Optimization (Gijon, Spain, June 18-21, 2024). Proceedings FGS2024, 116-123, https://digibuo.uniovi.es/dspace/handle/10651/74691
• Álvarez-López A., Slimane A.H. & Zuazua E. (2023) Interplay between depth and width for interpolation in neural ODEs, Neural Networks, 180(106640), https://doi.org/10.1016/j.neunet.2024.106640
• Coclite, G. M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua, E. (2023) Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave. Nonlinearity, 36(11), 5998–6019, https://doi.org/10.1088/1361-6544/acf01d
• Ftouhi, I. & Zuazua, E. (2023). Optimal design of sensors via geometric criteria. J. Geom. Anal., 33(253), https://doi.org/10.1007/s12220-023-01301-1
• Esteve Yagüe C, Geshkovski B, Pighin D, Zuazua Iriondo E (2021) Large-time asymptotics in deep learning. Hal-02912516v1f, arXiv:2008.02491