Francisco_Periago - Mulitphysic Simulation & Optimization Lab

Dr. Francisco Periago

Full Professor, Applied Mathematics

RESEARCH LINKS

OrcID: 0000-0002-7323-1809
Scopus Author ID: 14069164900
MathScinet: 1091151

ETSII Office B023. Campus Muralla del Mar. Hospital de Marina. C/ Dr. Fleming SN. 30202 Cartagena

Phone: +34 968338909

Email: [email protected]

Available For Postgraduate Supervision

ABOUT

I hold a Doctorate in Applied Mathematics from the University of Valencia, Spain, conferred in 1999. Notably, I served as the principal investigator in two I+D+i contracts with Navantia S.A (2007-2012), facilitating the funding of a predoctoral scholarship and a predoctoral research contract. This endeavor resulted in the submission of two PhD theses and the creation of the software SIMUSUB, presently employed at Navantia. Additionally, I have delivered keynote addresses at various national (e.g., XXVII CEDYA/XVII CMA, held in Zaragoza in 2022) and international congresses and workshops (e.g., at the esteemed Institute Henri Poincaré, Paris).

My academic engagements extend globally, having served as a visiting researcher at multiple esteemed institutions: (1) School of Mathematics, University of New South Wales (Australia, 3 months in 2000); (2) Instituto de Matemática - Laboratorio Nacional de Computación, Rio de Janeiro (Brazil, 6 weeks in 2003); (3) Departament de Mathématiques, Université de Franche-Comté (France, several short visits between 2006-2010); (4) École Polytechnique de Paris (France, several short visits between 2008-2014); (5) Mathematics Department, University of California, Santa Barbara (USA, 4 months in 2021). Furthermore, my research contributions have been recognized through successive periods of research activity (Sexenios de investigación y transferencia), totaling five periods, with the latest spanning from 2016 to 2021.

AREAS OF EXPERTISE

Optimal Control and Design of PDEs
Stochastic PDEs
Robust and Risk-averse design

Topology Optimization
Physics-informed Neural Networks
Shape control in Finite Strains

Book Access

PUBLICATIONS

19274/PI/14 21996/PI/22 Analysis Applied Mathematics Computational Mathematics Computational Mechanics Computational Theory and Mathematics Computer Graphics and Computer-Aided Design Computer Science Applications Constitutive modeling Control and Optimization Control and Systems Engineering DICOPMA Dielectric elastomer Evolutionary topology optimization Fail-safe design Finite element method General Engineering General Mathematics Management Science and Operations Research Mechanical Engineering Nonlinear electro-elasticity Numerical Analysis Ocean Engineering Phase-field Polyconvexity Rank-one laminates Robust design Software Topology optimisation 
Show all
2023
 García-Cervera, Carlos J.;  Kessler, Mathieu;  Periago, Francisco
Control of Partial Differential Equations via Physics-Informed Neural Networks Journal Article 
In: J Optim Theory Appl, vol. 196, no. 2, pp. 391–414, 2023, ISSN: 1573-2878.
Abstract | BibTeX | Tags: Applied Mathematics, Control and Optimization, Management Science and Operations Research | Links: 
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@article{García-Cervera2022,

title = {Control of Partial Differential Equations via Physics-Informed Neural Networks},

author = {Carlos J. García-Cervera and Mathieu Kessler and Francisco Periago},

url = {https://link.springer.com/content/pdf/10.1007/s10957-022-02100-4.pdf},

doi = {10.1007/s10957-022-02100-4},

issn = {1573-2878},

year  = {2023},

date = {2023-02-00},

urldate = {2023-02-00},

journal = {J Optim Theory Appl},

volume = {196},

number = {2},

pages = {391--414},

publisher = {Springer Science and Business Media LLC},

abstract = {<jats:title>Abstract</jats:title><jats:p>This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.</jats:p>},

keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},

pubstate = {published},

tppubtype = {article}

}

Close
<jats:title>Abstract</jats:title><jats:p>This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.</jats:p>
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2014
 Periago, Francisco
Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation Journal Article 
In: J Optim Theory Appl, vol. 161, no. 3, pp. 951–968, 2014, ISSN: 1573-2878.
BibTeX | Tags: Applied Mathematics, Control and Optimization, Management Science and Operations Research | Links: 
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@article{Periago2013,

title = {Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation},

author = {Francisco Periago},

doi = {10.1007/s10957-013-0447-9},

issn = {1573-2878},

year  = {2014},

date = {2014-06-00},

urldate = {2014-06-00},

journal = {J Optim Theory Appl},

volume = {161},

number = {3},

pages = {951--968},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},

pubstate = {published},

tppubtype = {article}

}

Close