KiLearn

KiLearn

Project name: KiLearn – Kinetic equations and Learning control
Project reference: PID2020-112617GB-C22
Funding source: MINECO
Duration: September 2021 – September 2024
Principal Investigator (PI): Miguel Escobedo (UPV/EHU), Enrique Zuazua (Deusto Foundation)

About the Project

KiLearn The project arises from the necessity to deepen the understanding of several fundamental questions in Machine Learning, quantum gases, and protein’s dynamics through a detailed study of the mathematical properties of some models that are currently used in those fields. These questions include the time evolution of a Bose-Einstein condensate, the fragmentation dynamics of proteins from experiments, or the impact of the architecture on the performances of a Neural Network.

The increasing interconnection between Machine Learning and kinetic theory motivates a research path that develops on the boundary between these two worlds and has the potential of leading to deep and breakthrough results in both areas. Starting from this hypothesis, the general objective of the research project KiLearn is to develop new Machine Learning-inspired mathematical tools for the analysis of Kinetic Equations and, at the same time, to extend the present knowledge in Machine Learning and Neural Networks taking advantage of the vast theoretical baggage that kinetic theory has to offer.

Project Members

-Miguel Escobedo – UPV/EHU, University of the Basque Country
Enrique Zuazua – Deusto Foundation
Umberto Biccari – Deusto Foundation
-Iker Pastor – University of Deusto

 

Publications

Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2021) Abstract: We analyze the interior ...
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Nonnegative control of finite-dimensional linear systems

Lohéac J., Trélat E., Zuazua E. Nonnegative control of finite-dimensional linear systems. Ann. I. H. Poincare-An., Vol. 38, No. 2, ...
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Local null controllability of a model system for strong interaction between internal solitary waves

Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto.  Local null controllability of a model system for strong interaction between ...
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The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms

M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in ...
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Controllability of one-dimensional viscous free boundary flows

B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim (2021), Vol. 59, No. 3, ...
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The turnpike property in semilinear control

D. Pighin The turnpike property in semilinear control ESAIM Control Optim. Calc. Var., Vol. 26 (2021), pp. 1-48 Abstract.An exponential ...
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The turnpike property in nonlinear optimal control – A geometric approach

N. Sakamoto, E. Zuazua. The turnpike property in nonlinear optimal control - A geometric approach. (2021) Automatica., Vol. 134 (2021), ...
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Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) ...
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Model predictive control with random batch methods for a guiding problem

Ko Dongnam, Zuazua Enrique. Model predictive control with random batch methods for a guiding problem (2021). Math. Models Methods Appl ...
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Averaged dynamics and control for heat equations with random diffusion

Bárcena J.A., Zuazua E.. Averaged dynamics and control for heat equations with random diffusion (2021) Syst. Control. Lett. Vol. 158 ...
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Sidewise control of 1-d waves

Y. Sarac, E. Zuazua. Sidewise control of 1-d waves. J Optim Theory Appl (2022). https://doi.org/10.1007/s10957-021-01986-w Abstract. We analyze the sidewise ...
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