Publications – cmc.deusto.eus

SHAP values through General Fourier Representations: Theory and Applications

R. Morales (2025) SHAP values through General Fourier Representations: Theory and Applications Abstract. This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that…

Spiking Neural Networks: a theoretical framework for Universal Approximation and training

U. Biccari (2025) Spiking Neural Networks: a theoretical framework for Universal Approximation and training Abstract. Spiking Neural Networks (SNNs) are widely regarded as a biologically-inspired and energy-efficient alternative to classical…

Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels

K. Lyu, U. Biccari, J. Wang (2025) Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels Abstract. This paper investigates the mean square exponential stabilization problem for a…

A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints

Roberto Morales, U. Biccari (2025) A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints, Abstract. This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization…

Sharp numerical approximation of the Hardy constant

L. Ignat, E. Zuazua (2025) Sharp numerical approximation of the Hardy constant Abstract. We study the P1 finite element approximation of the best constant in the classical Hardy inequality over…

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

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025) Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis, SIAM Mathematics of Data Science, SIMODS, arxiv: 2407.01602 Abstract. Transformers are…

A potential game perspective in Federated Learning

K. Liu, Z. Wang, E. Zuazua (2025) A potential game perspective in Federated Learning, arxiv:2411.11793 Abstract. Federated learning (FL) is an emerging paradigm for training machine learning models across distributed…

Regional and Partial Observability and Control of Waves

B. Dehman, S. Ervedoza, E. Zuazua (2025) Regional and Partial Observability and Control of Waves Abstract.We establish sharp regional observability results for solutions of the wave equation in a bounded…

Cluster-based classification with neural ODEs via control

A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2025) Optimized classification with neural odes via separability, J. Mach. Learn., arXiv:2312.13807v2 Abstract.We address binary classification using neural ordinary differential equations from the perspective…

Optimal convergence rates for the finite element approximation of the Sobolev constant

L. Ignat, E. Zuazua (2025) Optimal convergence rates for the finite element approximation of the Sobolev constant Abstract. We establish optimal convergence rates for the P1 finite element approximation of…

Boundary observation and control for fractional heat and wave equations

U. Biccari, E. Zuazua (2025) Boundary observation and control for fractional heat and wave equations, https://doi.org/10.48550/arXiv.2504.17413 Abstract. We establish boundary observability and control for the fractional heat equation over arbitrary…

Almost periodic turnpike phenomenon for time-dependent systems

S. Zamorano (2025)Almost periodic turnpike phenomenon for time-dependent systems Systems and Control Letters, Vol. 199, pp. 106069, https://doi.org/10.1016/j.sysconle.2025.106069 Abstract. This paper explores the turnpike behavior of a controlled system with…

Turnpike in optimal control and beyond: A survey

E. Trélat, E. Zuazua (2025)Turnpike in optimal control and beyond: A survey https://hal.science/hal-05002039 Abstract. The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide…

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

T. Crin-Barat, L. Liverani, Ly Shou, E. Zuazua (2025)Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach, arXiv:2503.00236 Abstract. We study the stability of one-dimensional linear hyperbolic systems…

Pointwise constraints for scalar conservation laws with positive wave velocity

N. De Nitti, D. Serre, E. Zuazua (2025) Pointwise constraints for scalar conservation laws with positive wave velocity Abstract. We consider a conservation law with strictly positive wave velocity and…

Gaussian Beam ansatz for finite difference wave equations

U. Biccari, E. Zuazua (2025) Gaussian Beam ansatz for finite difference wave equations, Found Comput Math. , Vol. 25, pp. 1–54, https://doi.org/10.1007/s10208-023-09632-9 Abstract. This work is concerned with the construction…

Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics

K. Liu, E. Zuazua (2025) Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics, Math. Models Methods Appl. Sci., Vol. 35, No. 6, pp. 1471-1521, arXiv:2412.01619v1, https://doi.org/10.1142/S0218202525500228 Abstract. In…

Exact Sequence Classification with Hardmax Transformers

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025) Exact Sequence Classification with Hardmax Transformers, arxiv: 2502.02270 Abstract. We prove that hardmax attention transformers perfectly classify datasets of $N$ labeled sequences…

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

T. Crin-Barat, N. De Nitti, E. Zuazua (2025) On the decay of one-dimensional locally and partially dissipated and hyperbolic systems, ESAIM:COCV, https://arxiv.org/abs/2206.00555 Abstract. We study the time-asymptotic behavior of linear…

Control of Hyperbolic and Parabolic Equations on Networks and Singular limits

J.A. Bárcena-Petisco, M. Cavalcante, G.M. Coclite, N. de Nitti, E. Zuazua (2025) Control of Hyperbolic and Parabolic Equations on Networks and Singular limits, MCRF, Vol. 15, No. 1, March 2025,…

FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning

Y. Song, Z. Wang, E. Zuazua (2025) FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning, Neural Networks, pp. 106-772, ISSN 0893-6080, https://doi.org/10.1016/j.neunet.2024.106772 Abstract. Federated learning (FL) is a promising…

Optimal L^p-approximation of convex sets by convex subsets

F. Zakaria, I. Ftouhi, E. Zuazua (2025) Optimal L^p-approximation of convex sets by convex subsets Abstract. Given a convex set Ω of R n, we consider the shape optimization problem…

Tracking controllability for the heat equation

J.A. Barcena-Petisco, E. Zuazua (2025) Tracking controllability for the heat equation, IEEE Trans. Autom. Control Abstract. We study the tracking or sidewise control- lability of the heat equation. More precisely,…

Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications

Z. Li, K. Liu, L. Liverani, E. Zuazua (2025)Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications, arXiv: 2407.17092 Abstract. In this paper, we introduce semi-autonomous neural ordinary…

Boundary sidewise observability of the wave equation

B. Dehman, E. Zuazua (2025) Boundary sidewise observability of the wave equation J. Eur. Math. Soc. (JEMS) Abstract. The wave equation on a bounded domain of Rn with non homogeneous…

Pattern control via diffusion interaction

D. Ruiz-Balet, E. Zuazua (2025) Pattern control via diffusion interaction Abstract. We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the…

Local Stability and Convergence of Unconstrained Model Predictive Control

D. Veldman, E. Zuazua (2025) Local Stability and Convergence of Unconstrained Model Predictive Control Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based…

Deep Neural Networks: Multi-Classification and Universal Approximation

M. Hernandez, E. Zuazua (2025)Deep Neural Networks: Multi-Classification and Universal Approximation arXiv:2409.06555 Abstract. We demonstrate that a ReLU deep neural network with a width of 2 and a depth of…

Approximate and Weighted Data Reconstruction Attack in Federated Learning

Z. Wang, Y. Song, E. Zuazua (2025) Approximate and Weighted Data Reconstruction Attack in Federated Learning arXiv:2308.06822 Abstract. Federated Learning (FL) is a distributed learning paradigm that enables multiple clients…

A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations

Z. Du, C.M. da Fonseca (2025) A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations, Journal of Computational and Applied Mathematics 461 (2025) 116429, 10.1016/j.cam.2024.116429 Abstract.…

Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation

A. Francisco, U. Biccari, E. Zuazua (2025)Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation Abstract. Inverse design of transport equations can be addressed by…

Observability for heat equations with time-dependent analytic memory

G. Wang, Y. Zhang, E. Zuazua (2024) Observability for heat equations with time-dependent analytic memory Arch Rational Mech Anal, Vol. 248, No. 115, https://doi.org/10.1007/s00205-024-02058-9 Abstract. This paper presents a complete…

Progress and future directions in machine learning through control theory

E. Zuazua (2024) Progress and future directions in machine learning through control theory Proceedings book FGS 2024, pp. 116, https://hdl.handle.net/10651/74677 Abstract. This paper presents our recent advancements at the intersection…

Optimized classification with neural odes via separability

A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2024)Optimized classification with neural odes via separability Neural Networks, Vol. 180, 106640, arXiv:2312.13807 Abstract. Classification of N points becomes a simultaneous control problem when…

Stability and Convergence of a Randomized Model Predictive Control Strategy

D.W.M. Veldman, A. Borkowski, E. Zuazua (2024) Stability and Convergence of a Randomized Model Predictive Control Strategy , IEEE Trans. Automat., Vol. 69, No. 9, pp. 6253-6260 Abstract. This paper is…

Exact Controllability and Stabilization of the Wave Equation

E. Zuazua. Exact Controllability and Stabilization of the Wave Equation (2024) UNITEXT (La Matematica per il 3+2, UNITEXTMAT) - Springer Cham, Vol. 162, No. 1, eBook ISBN 978-3-031-58857-0, https://link.springer.com/book/10.1007/978-3-031-58857-0, arxiv:2402.17894…

Control and Machine Learning

E. Zuazua (2024) Control and Machine Learning Proceedings of the 9th. International Conference on Control and Optimization with Industrial Applications, August 27-29, 2024, Istanbul, Turkey Abstract. In this talk, we…

Eigenvalue bounds for the Gramian operator of the heat equation

M. Lazar, E. Zuazua. Eigenvalue bounds for the Gramian operator of the heat equation (2024) Automatica, Vol. 164, pp. 111-653, https://doi.org/10.1016/j.automatica.2024.111653 Abstract. This paper is concerned with the eigenvalue decay…

Finite element approximation of the Hardy constant

F. Della Pietra, G. Fantuzzi, LI Ignat, AL Masiello, G. Paoli, E. Zuazua (2024)Finite element approximation of the Hardy constant J. Convex Anal. Special Issue Giuseppe Buttazzo 70 Abstract. We…

Control of neural transport for normalising flows

D. Ruiz-Balet, E. Zuazua (2024)Control of neural transport for normalising flows J. Math. Pures Appl., Vol. 181, pp. 58-90, ISSN 0021-7824. https://doi.org/10.1016/j.matpur.2023.10.005 Abstract. Inspired by normalizing flows, we analyze the…

Tracking controllability for finite-dimensional linear systems

S. Zamorano, E. Zuazua (2025)Tracking controllability for finite-dimensional linear systems arXiv:2407.18641v2 Abstract. In this work, we present a functional analytic framework for tracking controllability in finite-dimensional linear systems. By leveraging…

Averaged observations and turnpike phenomenon for parameter-dependent systems

M. Hernandez, M. Lazar, S. Zamorano (2024) Averaged observations and turnpike phenomenon for parameter-dependent systems arXiv:2404.17455 Abstract. Our main contribution in this article is the achievement of the turnpike property…

Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings

GM. Coclite, N. De Nitti, F. Maddalena, G. Orlando, E. Zuazua (2025) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings, Mathematical Models and Methods…

The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries,

C.M. da Fonseca, C. Kızılateş, N. (2024) The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries, Logic Journal of the IGPL, jzae065, 10.1093/jigpal/jzae065…

Revisiting some r-Fibonacci sequences and Hessenberg matrices

C.M. da Fonseca, P. Saraiva, A.G. Shannon (2024) Revisiting some -Fibonacci sequences and Hessenberg matrices, Notes on Number Theory and Discrete Mathematics, Vol. 30, pp. 704-715, 10.7546/nntdm.2024.30.4.704-715 Abstract. The relationship…

A new generalization of min and max matrices and their reciprocals counterparts

C.M. da Fonseca, C. Kızılateş, N. (2024) A new generalization of min and max matrices and their reciprocals counterparts, Filomat, Vol. 38, pp. 421-435, 10.2298/FIL2402421F Abstract. In this paper, we…

Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner’s composition principle

M. Anđelić, C.M. da Fonseca (2024) Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner's composition principle, Discrete Mathematics Letters, Vol. 14, pp. 108-117, 10.47443/dml.2024.160 Abstract. The notion of equitable…

On Chebyshev polynomials and the inertia of certain matrices

K. Castillo, C.M. da Fonseca, J. Petronilho (2024) On Chebyshev polynomials and the inertia of certain matrices, Applied Mathematics and Computation, Vol. 467, pp. 128-497, 10.1016/j.amc.2023.128497 Abstract. It was first…

Optimal Placement and Shape Design of Sensors via Geometric Criteria

I. Ftouhi, E. Zuazua (2024) Optimal Placement and Shape Design of Sensors via Geometric Criteria, 2024 European Control Conference (ECC), Stockholm, Sweden, 2024, pp. 834-837, doi: 10.23919/ECC64448.2024.10591236 Abstract. The optimal…

Control of a Lotka-Volterra System with Weak Competition

M. Sonego, E. Zuazua (2024)Control of a Lotka-Volterra System with Weak Competition, arXiv:2409.20279 Abstract. The Lotka-Volterra model reflects real ecological interactions where species com- pete for limited resources, potentially leading…

Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

H. Antil, U. Biccari, R. Ponce, M. Warma, S. Zamorano (2024) Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation, Vol. 13, pp. 893-924, https://doi.org/10.3934/eect.2024010…

Random Batch Method (RBM) and Model Predictive Control (MPC) for Converter-Dominated Power Systems

C. Vázquez. Random Batch Method (RBM) and Model Predictive Control (MPC) for Converter-Dominated Power Systems (2024) Abstract. This paper investigates the application of Data-based Reduced Order Models, the Random Batch…

A formal operator involving Fermatian numbers

C.M. da Fonseca, A.G. Shannon (2024) A formal operator involving Fermatian numbers, Notes on Number Theory and Discrete Mathematics, Vol. 30, pp. 491-498, 10.7546/nntdm.2024.30.3.491-498 Abstract. In this note, old and…

The generating function of a bi-periodic Leonardo sequence

C.M. da Fonseca (2024) The generating function of a bi-periodic Leonardo sequence, Armenian Journal of Mathematics, Vol. 16, pp. 1-8, 10.52737/18291163-2024.16.07-1-8 Abstract. In "A note on bi-periodic Leonardo sequence", the…

The determinants of certain double banded (0,1) Toeplitz matrices

Z. Du, C.M. da Fonseca (2023) The determinants of certain double banded (0,1) Toeplitz matrices, Miskolc Mathematical Notes, Vol. 24, pp.1307-1315, 10.18514/MMN.2023.4053 Abstract. We prove a conjecture proposed recently in…

On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence

C.M. da Fonseca, A.G. Shannon (2023) On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence, Notes on Number Theory and Discrete Mathematics, Vol.…

The number of P-vertices for acyclic matrices with given nullity

Z. Du, C.M. da Fonseca (2023) The number of P-vertices for acyclic matrices with given nullity, Discrete Mathematics, Vol. 346, pp.113-592, 10.1016/j.disc.2023.113592 Abstract. In this paper, we completely characterize those…

The characterization of the minimal weighted acyclic graphs

Z. Du, C.M. da Fonseca (2023) The characterization of the minimal weighted acyclic graphs, Linear Algebra and its Applications, Vol. 672, pp.75-92, 10.1016/j.laa.2023.04.019 Abstract. In this paper, we completely characterize…

Further developments of basic trigonometric power sums

Z. Du, C.M. da Fonseca, V. Kowalenko (2023) Further developments of basic trigonometric power sums, RACSAM Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas,…

Chain graph sequences and Laplacian spectra of chain graphs

A. Alazemi, M. Anđelić, K. Chandra, Carlos M. da Fonseca (2023) Chain graph sequences and Laplacian spectra of chain graphs, Linear and Multilinear Algebra, Vol. 74, pp.569-585, 10.1080/03081087.2022.2036672 Abstract. A…

Root location for the characteristic polynomial of a Fibonacci type sequence

Z. Du, C.M. da Fonseca (2023) Root location for the characteristic polynomial of a Fibonacci type sequence, Czechoslovak Mathematical Journal, Vol. 73, pp. 189-195, 10.21136/CMJ.2022.0043-22 Abstract. We analyse the roots…

A second-order difference equation with sign-alternating coefficients

M. Anđelić, C.M. da Fonseca, T. Koledin, Z. Stanić (2022) A second-order difference equation with sign-alternating coefficients, Kuwait Journal of Science, Vol. 50, No. 1, 10.48129/kjs.20425 Abstract. We provide an…

An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs

M. Anđelić, C.M. da Fonseca, T. Koledin, Z. Stanić (2022) An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs, Journal of Applied Mathematics and Computing 69 (2023) 491-503,…

A periodic determinantal property for (0,1) double banded matrices

Z. Du, C.M. da Fonseca (2022) A periodic determinantal property for (0,1) double banded matrices, Linear and Multilinear Algebra, Vol. 70, pp. 5316-5328, 10.1080/03081087.2021.1913980 Abstract. In this paper, we extend…

An identity involving derangement numbers and Bell numbers

Z. Du, C.M. da Fonseca (2022) An identity involving derangement numbers and Bell numbers, Applicable Analysis and Discrete Mathematics, Vol. 16, pp.485-494, 10.2298/AADM200705018D Abstract. The aim of this paper is…

On tridiagonal matrices associated with Jordan blocks

C.M. da Fonseca, V. Kowalenko (2022) On tridiagonal matrices associated with Jordan blocks, Acta Universitatis Sapientiae, Mathematica, Vol. 14, pp.61-74, 10.2478/ausm-2022-0004 Abstract. This paper aims to show how some standard…

A Sylvester-Kac matrix type and the Laplacian controllability of half graphs

M. Anđelić, C.M. da Fonseca, E. Kılıç, Z. Stanic (2022) New strong divisibility sequences, Electronic Journal of Linear Algebra, Vol. 38, pp. 559-571, 10.13001/ela.2022.6947 Abstract. In this paper, we provide…

New strong divisibility sequences

Z. Du, C.M. da Fonseca, D. Dimitrov (2022) New strong divisibility sequences, Ars Mathematica Contemporanea, Vol. 22, P1.08, 10.26493/1855-3974.2473.f2e Abstract. We provide new families of divisibility and strong divisibility sequences…

The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach

Milica Anđelić, C.M. da Fonseca, Fatih Yılmaz (2022) Determinantal representations for the number of subsequences without isolated odd terms, Heliyon, Vol. 8, E08863, 10.1016/j.heliyon.2022.e08863 Abstract. In this note we consider…

Determinantal representations for the number of subsequences without isolated odd terms

Milica Anđelić, C.M. da Fonseca (2021) Determinantal representations for the number of subsequences without isolated odd terms, Notes on Number Theory and Discrete Mathematics 27 (2021) 116-121, 10.7546/nntdm.2021.27.4.116-121 Abstract. In…

On the constant coefficients of a certain recurrence relation: A simple proof

Milica Anđelić, C.M. da Fonseca (2021) On the constant coefficients of a certain recurrence relation: A simple proof, Heliyon, Vol. 7, E07764, 10.1016/j.heliyon.2021.e07764 Abstract. In this note, we provide a…

The spectrum of a new class of Sylvester-Kac matrices

A. Alazemi, C.M. da Fonseca, E. Kılıç (2021) The spectrum of a new class of Sylvester-Kac matrices, Filomat, Vol. 35, pp.4017-4031, 10.2298/FIL2112017A Abstract. We define a new class of Sylvester-Kac…

Disproving a conjecture of Thornton on Bohemian matrices

Z. Du, C.M. da Fonseca, Y. Xu, J. Ye (2021) Disproving a conjecture of Thornton on Bohemian matrices, Open Mathematics, Vol. 19, pp. 505-514, 10.1515/math-2021-0045 Abstract. In this paper, we…

Three representation types for systems of forms and linear maps

A. Alazemi, M. Anđelić, C.M. da Fonseca, V. Futorny, V.V. Sergeichuk (2021) Three representation types for systems of forms and linear maps, Mathematics, Vol. 9, No. 455, 10.3390/math9050455 Abstract. We…

Interplay between depth and width for interpolation in neural ODEs

A. Alvarez-Lopez, A. Hadj Slimane, E. Zuazua (2024) Interplay between depth and width for interpolation in neural ODEs, Neural Networks, Vol. 180, pp. 106-640, https://doi.org/10.1016/j.neunet.2024.106640, ISSN 0893-6080 Abstract. Neural ordinary…

FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning

E. Zuazua. FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning (2024) https://doi.org/10.48550/arXiv.2402.13989 Abstract. Federated learning (FL) is a promising framework for learning from distributed data while maintaining privacy. The…

Fourier series and sidewise control of 1-d waves

E. Zuazua. Fourier series and sidewise control of 1-d waves (2024) Volume in honor of Yves Meyer, Documents Mathématiques of the French Mathematical Society (SMF), Vol. 22, p. 341-365, arXiv:2308.04906…

Uniform Turnpike Property and Singular Limits

M Hernandez-Salinas, E. Zuazua (2024) Uniform Turnpike Property and Singular Limits Acta Appl. Math., Vol. 190, No. 3, https://doi.org/10.1007/s10440-024-00640-7 Abstract. Motivados por límites singulares para problemas de control óptimo a…

Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system

T. Crin-Barat, E. Zuazua. Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: Application to the nonlinearly damped p-system (2024) Ann. Inst. Henri Poincare (C) Anal. Non Lineaire,…

Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements

R. Lecarós, J. Lopez-Rios, G.I. Montecinos, E. Zuazua. Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements, (2024) Math. Meth. Appl. Sci., pp. 1–32, https://doi.org/10.1002/mma.10251…

Large-time asymptotics in deep learning

C. Esteve, B. Geshkovski, D. Pighin, E. Zuazua (2025) Large-time asymptotics in deep learning, https://hal.archives-ouvertes.fr/hal-02912516 Abstract. We consider the neural ODE perspective of supervised learning and study the impact of the…

Special Issue Dedicated to the Memory of Professor Roland Glowinski

A. Quaini, X. Qin, X. Tai, E. Zuazua (2025)Special Issue Dedicated to the Memory of Professor Roland Glowinski, AMSA, Vol. 8, No. 3, pp. 407 – 409 8 articles in:…

Control of reaction-diffusion models in biology and social sciences

D. Ruiz-Balet, E. Zuazua (2024) Control of reaction-diffusion models in biology and social sciences Math. Control Relat. Fields, Vol. 12, No. 4, pp. 955-1038, https://doi.org/10.3934/mcrf.2022032 Abstract. These lecture notes address…

Sidewise Control

E. Zuazua (2023) Sidewise Control "Control methods in Hyperbolic PDEs", Oberwolfach, November 2023, DOI:10.4171/OWR/2023/52, pp. 62-63 "Inspired on [1] and [4], we explored the lateral or sidewise control properties of…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

C. Esteve, E. Zuazua. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws Nonlinear Analysis, Vol. 227, https://doi.org/10.1016/j.na.2022.113167 Abstract. We give a full characterization of the range…

Constrained control of gene-flow models

I. Mazari, D. Ruiz-Balet, E. Zuazua (2023)Constrained control of gene-flow models, Ann. Inst. Henri Poincare (C) Anal. Non Lineaire ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to the transfer…

Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

G.M. Coclite, N. De Nitti, E. Zuazua (2023) Long-time convergence of a nonlocal Burgers' equation towards the local N-wave, CVGMT Nonlinearity, Vol. 36, No. 11, pp. 5998-6019, DOI: 10.1088/1361-6544/acf01d Abstract.…

Greedy search of optimal approximate solutions

M. Lazar, E. Zuazua (2023) Greedy search of optimal approximate solutions Pure and Applied functional Analysis, Vol. 8, No. 2, pp. 547-564, http://yokohamapublishers.jp/online2/oppafa/vol8/p547.html Abstract. In this paper we develop a…

Multilevel control by duality

U. Biccari, E. Zuazua (2023) Multilevel control by duality Systems & Control Letters, Vol. 175, 105-502, https://doi.org/10.1016/j.sysconle.2023.105502 Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing…

Neural ODE Control for Classification, Approximation and Transport

D. Ruiz-Balet, E. Zuazua (2023)Neural ODE Control for Classification, Approximation and Transport, SIAM Review, Vol. 65, No. 3, pp. 735-773, https://doi.org/10.1137/21M1411433 Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from…

A quantitative analysis of Koopman operator methods for system identification and predictions

C. Zhang, E. Zuazua (2023) A quantitative analysis of Koopman operator methods for system identification and predictions, Comptes Rendus. Mécanique, Vol. 351, No. S1, pp. 1-31. In memory of R.…

Optimal design of sensors via geometric criteria

I. Ftouhi, E. Zuazua (2023) Optimal design of sensors via geometric criteria, J. Geom. Anal., Vol. 33, No. 253, https://doi.org/10.1007/s12220-023-01301-1 Abstract. We consider a convex set Ω and look for…

Boundary Controllability for the 1D Moore-Gibson-Thompson equation

C. Lizama, S. Zamorano (2023) Boundary Controllability for the 1D Moore-Gibson-Thompson equation, Meccanica 58, Vol. 58, pp. 1031-1038, 10.1007/s11012-022-01551-3. https://link.springer.com/article/10.1007/s11012-022-01551-3 Abstract. This article addresses the boundary controllability problem for a…

Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields

M. Hernandez, R. Lecaros, S. Zamorano (2023) Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields , Vol. 365, pp. 808-832, https://www.aimsciences.org/article/doi/10.3934/mcrf.2022016 Abstract. This…

Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions

R. Lecaros, R. Morales, A. Pérez, S. Zamorano (2023) Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions, Differ. Equ., Vol. 365, pp.…