Publications - Mulitphysic Simulation & Optimization Lab

19274/PI/14 21996/PI/22 Analysis Applied Mathematics Computational Mathematics Computational Mechanics Computer Graphics and Computer-Aided Design Computer Science Applications Control and Optimization Control and Systems Engineering DICOPMA Dielectric elastomer Dielectric elastomers Electro-active polymer Energy–momentum scheme Evolutionary topology optimization Fail-safe design Finite element method General Engineering General Mathematics Mechanical Engineering Nonlinear electro-elasticity Numerical Analysis Ocean Engineering Phase-field PID2022-141957OA-C22 Polyconvexity Rank-one laminates Software Topology optimisation 
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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}

}

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<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}

}

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