I'm an assistant professor of mathematics in the Centre for Analysis, Scientific Computing and Applications at TU/e (Eindhoven University of Technology). My work deals with the numerical analysis of kinetic equations and other partial differential equations (PDEs). I'm also interested in collective dynamics, self-organisation, and the control of agent-based models.
Prior to my current post, I was a research associate at the University of Oxford, affiliated with the Oxford Centre for Nonlinear Partial Differential Equations at the Mathematical Institute. I also worked as a postdoctoral researcher at the Université de Lille with the ANEDP and Inria RAPSODI groups, under the supervision of Thomas Rey. I earned my doctorate at Imperial College London, where my advisors were José Antonio Carrillo and Pierre Degond.
My TU/e site can be found here.
Rafael Bailo · José Antonio Carrillo · Andrea Medaglia · Mattia Zanella
Multiscale Modeling and Simulation, 2024 (to appear).
Multiscale Modeling and Simulation, 2024 (to appear).
@Article{BCM2024,
title={Uncertainty quantification for the homogeneous {L}andau-{F}okker-{P}lanck equation via deterministic particle {G}alerkin methods},
author={Bailo, Rafael and Carrillo, José Antonio and Medaglia, Andrea and Zanella, Mattia},
journal={Multiscale Model. Sim. (to appear)},
year={2024},
doi={10.48550/arXiv.2312.07218},
archivePrefix={arXiv},
arXivId={2312.07218},
eprint={2312.07218},
}
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a sg representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a sg representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.
Rafael Bailo
José Antonio Carrillo
Jingwei Hu
Rafael Bailo · José Antonio Carrillo · Jingwei Hu
Journal of Plasma Physics, 90 (4), 2024.
Journal of Plasma Physics, 90 (4), 2024.
@Article{BCH2024,
title={The collisional particle-in-cell method for the {V}lasov-{M}axwell-{L}andau equations},
author={Bailo, Rafael and Carrillo, José Antonio and Hu, Jingwei},
journal={J. Plasma Phys.},
year={2024},
doi={10.1017/S0022377824001077},
volume={90},
number={4},
archivePrefix={arXiv},
arXivId={2401.01689},
eprint={2401.01689},
}
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.
Rafael Bailo · Alethea Barbaro · Susana N. Gomes · Konstantin Riedl · Tim Roith · Claudia Totzeck · Urbain Vaes
Journal of Open Source Software, 9 (98), 2024.
Journal of Open Source Software, 9 (98), 2024.
@Article{BBG2024,
title={{CBX}: {P}ython and {J}ulia packages for
consensus-based interacting particle methods},
author={Bailo, Rafael and Barbaro, Alethea and Gomes, Susana N. and Riedl, Konstantin and Roith, Tim and Totzeck, Claudia and Vaes, Urbain},
journal={Journal of Open Source Software},
year={2024},
doi={10.21105/joss.06611},
volume={9},
number={98},
archivePrefix={arXiv},
arXivId={2403.14470},
eprint={2403.14470},
}
We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimisation methods (CBO) for global, derivative-free optimisation. The raison d'être of our libraries is twofold: on the one hand, to offer high-performance implementations of CBX methods that the community can use directly, while on the other, providing a general interface that can accommodate and be extended to further variations of the CBX family. Python and Julia were selected as the leading high-level languages in terms of usage and performance, as well as their popularity among the scientific computing community. Both libraries have been developed with a common ethos, ensuring a similar API and core functionality, while leveraging the strengths of each language and writing idiomatic code.
We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimisation methods (CBO) for global, derivative-free optimisation. The raison d'être of our libraries is twofold: on the one hand, to offer high-performance implementations of CBX methods that the community can use directly, while on the other, providing a general interface that can accommodate and be extended to further variations of the CBX family. Python and Julia were selected as the leading high-level languages in terms of usage and performance, as well as their popularity among the scientific computing community. Both libraries have been developed with a common ethos, ensuring a similar API and core functionality, while leveraging the strengths of each language and writing idiomatic code.