optimal control

Sparse approximation in learning via neural ODEs

deep learning, Neural ODEs, Nonlinear systems, optimal control, Sparsity, Supervised Learning

Esteve C., Geshkovski B. Sparse approximation in learning via neural ODEs (2021) Abstract. We consider the continuous-time, neural ordinary differential equation (neural ODE) perspective of deep supervised learning, and study the…

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

descriptor systems, linear systems, long time behavior, optimal control, Riccati equations

Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) SIAM J. Control Optim., Vol. 59.5 (2021), pp. 3600-3624 Abstract.…

The turnpike property in nonlinear optimal control – A geometric approach

Nonlinear system, optimal control, Turnpike

N. Sakamoto, E. Zuazua. The turnpike property in nonlinear optimal control - A geometric approach. (2021) Automatica., Vol. 134 (2021), p. 109939 Abstract: This paper presents, using dynamical system theory,…

Large-time asymptotics in deep learning

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

Esteve C., Geshkovski B., Pighin D., Zuazua E. Large-time asymptotics in deep learning (2021). hal-02912516 Abstract. It is by now well-known that practical deep supervised learning may roughly be cast as…

Sparse source identification of linear diffusion–advection equations by adjoint methods

Adjoint problem, Diffusion–advection equation, Inverse problems, optimal control, Optimization

Monge A., Zuazua E. Sparse source identification of linear diffusion–advection equations by adjoint methods. Syst. Control. Lett, vol. 145 (2020). DOI: https://doi.org/10.1016/j.sysconle.2020.104801 Abstract: We present an algorithm for the time-inversion…

Turnpike Control and Deep Learning by Enrique Zuazua at IITK

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

Worldwide. 08.09.2020. Yesterday, our Head Enrique Zuazua gave a talk about "Turnpike Control and Deep Learning" hosted by IITK - Indian Institute of Technology, Kampur in collaboration with IISER-Kolkata, IISER-Pune,…

Turnpike Control and Deep Learning at IITK by E. Zuazua

Next tuesday September 8th, our Head Enrique Zuazua will present "Turnpike Control and Deep Learning" on the IITK research seminars organized by IITK- Indian Institute of Technology, Kanpur in collaboration with…

Turnpike Control and Deep Learning – Fields Institute 2nd Simposium on Machine Learning and Dynamical Systems

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

Worldwide. 01.09.2020. The Fields Institute for Research in Mathematical Sciences at the University of Toronto, Canada organized the Second Simposium on Machine Learning and Dynamical Systems on September 21st to…

A stochastic approach to the synchronization of coupled oscillators

coupled oscillators, gradient descent, Kuramoto model, optimal control, random batch method, synchronization

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020). DOI: 10.3389/fenrg.2020.00115 Abstract. This paper…

Asymptotic behavior and control of a “guidance by repulsion” model

Asymptotic stability, Collective behavior, Guidance by repulsion, Herding, optimal control

Dongnam Ko, E. Zuazua, Asymptotic behavior and control of a "guidance by repulsion" model. Math Models Methods Appl. Sci. Vol. 30, No. 04, pp. 765-804 (2020).DOI:10.1142/S0218202520400047 Abstract. We model and…

Sparse approximation in learning via neural ODEs

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

The turnpike property in nonlinear optimal control – A geometric approach

Large-time asymptotics in deep learning

Sparse source identification of linear diffusion–advection equations by adjoint methods

Turnpike Control and Deep Learning by Enrique Zuazua at IITK

Turnpike Control and Deep Learning at IITK by E. Zuazua

Turnpike Control and Deep Learning – Fields Institute 2nd Simposium on Machine Learning and Dynamical Systems

A stochastic approach to the synchronization of coupled oscillators

Asymptotic behavior and control of a “guidance by repulsion” model

Nonuniqueness of minimizers for semilinear optimal control problems

The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

A framework for randomized time-splitting in linear-quadratic optimal control

Numerical Control: Part A

Numerical hypocoercivity for the Kolmogorov equation