Associated Researcher
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| My research interests include the analysis, simulation, and control of dynamical systems and, more recently, the mathematical foundations of Machine Learning and the integration of Artificial Intelligence into control theory and dynamical modeling. | |||||
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Associated Researcher at DeustoTech, University of Deusto, Basque Country, Spain. Former postdoctoral researcher at DeustoTech (2017-2022) and AI researcher at Sherpa.ai (2022–2024).
I got my PhD summa cum laude from the University of the Basque Country (EHU) in 2016, within the ERC project NUMERIWAVES.
My research interests include the analysis, simulation, and control of dynamical systems and, more recently, the mathematical foundations of Machine Learning and the integration of Artificial Intelligence into control theory and dynamical modeling. Specifically, my expertise covers:
- Control theory for nonlocal PDE models, such as hyperbolic, parabolic, and dispersive fractional equations, memory-type dynamics, and PDEs with integral potentials;
- Numerical analysis for local and nonlocal PDEs with control or optimization purposes;
- Stochastic and data-driven approaches to control and optimization problems;
- Integration of ML with control theory, focusing on learning-based feedback design and hybrid mathematical–AI frameworks;
- Mathematical analysis of learning algorithms, exploring their structure through tools from dynamical systems, optimal control, and variational analysis.
My research activities also include collaborations in electrical and control engineering, particularly on the modeling, stability analysis, and control of power grids, developed jointly with the University of Mondragón and several industrial partners in the Basque Country. More recently, I have become involved in biomedical research projects, where I apply mathematical modeling and AI-based methodologies to the study of healthy aging.
- Ph. D summa cum laude in Mathematics (Sep 2013 – Dec 2016), University of the Basque Country and BCAM – Basque Center for Applied Mathematics, Bilbao, Spain.
- Internship (Mar 2013 – Aug 2013), BCAM – Basque Center for Applied Mathematics, Bilbao, Spain, ERC Advanced Grant FP7-246775 NUMERIWAVES.
- Master degree in applied mathematics (2010 – 2012), University of Florence, Italy.
- Bachelor’s Degree in Mathematics (2007 – 2010), University of Florence, Italy.
PhD's Thesis. On the controllability of Partial Differential Equations involving non-local terms and singular potentials
Advisor: Prof. Enrique Zuazua – FAU (Erlangen-Nürnberg, Germany), Deusto Foundation-University of Deusto (Bilbao, Basque Country, Spain) and UAM (Madrid, Spain)
Description: In this thesis we study the controllability and observability of certain types of Partial Differential Equations, that describes several phenomena arising in many fields of the applied sciences, such as elasticity theory, ecology, anomalous transport and diffusion, material science, filtration in porus media and quantum mechanics. In particular, we focus on the analysis of PDEs with non-local and singular terms. View the PhD thesis
Master's Thesis. A free boundary problem for the CaCO3 neutralisation of acid waters
Advisors: Prof. Riccardo Ricci and Dr. Angiolo Farina – University of Florence, Italy
Description: In this thesis, we analyze a parabolic free boundary model arising from a problem of neutralization of acid waters via the filtration through calcium carbonate. After having developed the model according to the Physics, we computed an approximate but reliable solution, investigating its properties and its asymptotic behavior. This analysis has been repeated also in cylindrical and spherical geometry, both configurations being relevant in the description of the physical phenomena at the basis of our model.
Released
Boundary observation and control for fractional heat and wave equations
Gaussian Beam ansatz for finite difference wave equations
Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
Multilevel control by duality
A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
Multiplicity of solutions for fractional q(.)-Laplacian equations
Multilevel Selective Harmonic Modulation via Optimal Control
Control and Numerical approximation of Fractional Diffusion Equations
Internal control for a non-local Schrödinger equation involving the fractional Laplace operator
A stochastic approach to the synchronization of coupled oscillators
Accepted
Submitted
Spiking Neural Networks: a theoretical framework for Universal Approximation and training
Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels
A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints
Boundary observation and control for fractional heat and wave equations
Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation
Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion
Null Controllability for a Degenerate Structured Population Model
Optimal control of linear non-local parabolic problems with an integral kernel
Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation
Stochastic optimization methods for the simultaneous control of parameter-dependent systems
- Moving control strategy for memory-type equations
- Stochastic optimization for simultaneous control
- Synchronized Oscillators
- An eulerian-lagrangian scheme for the problem of the inverse design of hyperbolic transport equations
- Simulation of Fractional Heat Equation
- Propagation of one and two-dimensional discrete waves under finite difference approximation
- Finite Element approximation of the one-dimensional fractional Laplacian
- Controllability of the one-dimensional fractional heat equation under positivity constraints
- WKB expansion for a fractional Schrödinger equation with applications to controllability
- LQR control of a fractional reaction diffusion equation
- 20.11.2025 Deep Operator Networks in Control Theory: Concepts and Applications, FAU MoD/GMU workshop: The Mathematics of Scientific Machine Learning and Digital Twins PDF Slides
- 20.06.2022 FAU DCN-AvH Mini workshop: Recent advances: (Multilevel Control), FAU - Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany PDF Slides
- 31.01.2020 Controllability of Fractional Heat Equations under Positivity Constraints, 5th. Congress of young researchers RSME, Castelló, Spain, PDF Slides
- 21.08.2019 Controllability of the 1d fractional heat equation under positivity constraints, 8th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain | PDF Slides
- 03.04.2019 Dynamics and control for multi-agent networked systems, Universidad de Cantabria, Santander, Spain | PDF Slides
- 14.03.2019 Dynamics and control for multi-agent networked systems, Friedrich-Alexander Universität, FAU Erlangen-Nürnberg, Germany | PDF Slides
- 05.12.2018 Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, 1st workshop on dynamics, control and numerics for fractional PDE’s, San Juan, Puerto Rico | PDF Slides
- 30.08.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, 14th French-Romanian conference in applied mathematics, Bordeaux, France | PDF Slides
- 06.07.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, University of Craiova, Romania | PDF Slides
- 01.03.2018 Controllability of Partial Differential Equations with integral kernels, MINAKE 2018 – Microlocal and Numerical Analysis, Kinetic Equations Control Conference, Madrid, Spain | PDF Slides
- 29.08.2017 Finite Element approximation of the one-dimensional fractional Poisson equation with applications to numerical control, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain | PDF Slides
- 25.08.2017 Control of partial differential equations involving the fractional Laplacian, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain, PDF Slides
- 08.03.2017 Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function, Universidad Autónoma de Madrid, Spain.
- Ph. D summa cum laude in Mathematics (Sep 2013 – Dec 2016), University of the Basque Country and BCAM – Basque Center for Applied Mathematics, Bilbao, Spain.
- Internship (Mar 2013 – Aug 2013), BCAM – Basque Center for Applied Mathematics, Bilbao, Spain, ERC Advanced Grant FP7-246775 NUMERIWAVES.
- Master degree in applied mathematics (2010 – 2012), University of Florence, Italy.
- Bachelor’s Degree in Mathematics (2007 – 2010), University of Florence, Italy.
PhD's Thesis. On the controllability of Partial Differential Equations involving non-local terms and singular potentials Advisor: Prof. Enrique Zuazua – FAU (Erlangen-Nürnberg, Germany), Deusto Foundation-University of Deusto (Bilbao, Basque Country, Spain) and UAM (Madrid, Spain) Description: In this thesis we study the controllability and observability of certain types of Partial Differential Equations, that describes several phenomena arising in many fields of the applied sciences, such as elasticity theory, ecology, anomalous transport and diffusion, material science, filtration in porus media and quantum mechanics. In particular, we focus on the analysis of PDEs with non-local and singular terms. View the PhD thesis Master's Thesis. A free boundary problem for the CaCO3 neutralisation of acid waters Advisors: Prof. Riccardo Ricci and Dr. Angiolo Farina – University of Florence, Italy Description: In this thesis, we analyze a parabolic free boundary model arising from a problem of neutralization of acid waters via the filtration through calcium carbonate. After having developed the model according to the Physics, we computed an approximate but reliable solution, investigating its properties and its asymptotic behavior. This analysis has been repeated also in cylindrical and spherical geometry, both configurations being relevant in the description of the physical phenomena at the basis of our model.
Academic Courses
- 01.09.2024 - 31.01.2025.Calculus, Bachelor degree in Computer Engineering, (6 ECTS), University of Deusto, Bilbao campus, Spain
- 01.09.2023 - 31.01.2024.Algebra, Bachelor degree in Industrial Engineering, (6 ECTS), University of Deusto, Bilbao campus, Spain
- 01.09.2021 - 31.01.2022. Algebra, Bachelor degree in Computer Engineering, (6 ECTS), University of Deusto, Bilbao campus, Spain
Other Courses
- 01.08.2022 - 12.08.2022.Course on Numerical methods for fractional equation control and optimization, University of Shangai (online)
Certificates
- IKERTRAMOS call 2019: positive evaluation of the Agencia de Calidad del Sistema Universitario Vasco (UNIBASQ) for the research activity in the 6 years period 2013-2018
- PROFESOR DE UNIVERSIDAD PRIVADA: positive evaluation of Aneca for the role of professor of private university" y "CONTRATADO DOCTOR: positive evaluation of Aneca for the role of tenured professor