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.

Recent Publications

header
Hello, world! This is a toast message.

Uncertainty quantification for the homogeneous Landau-Fokker-Planck equation via deterministic particle Galerkin methods

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.

header
Hello, world! This is a toast message.

The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations

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.

header
Hello, world! This is a toast message.

CBX: Python and Julia packages for consensus-based interacting particle methods

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.