I'm an assistant professor in the Centre for Analysis, Scientific Computing and Applications at TU/e (Eindhoven University of Technology), in the group of Olga Mula. 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.

Recent Publications

header
Hello, world! This is a toast message.

Aggregation-diffusion equations for collective behaviour in the sciences

arXiv: 2405.16679, 2024.

arXiv: 2405.16679, 2024.

@Article{BCG2024
	title={Aggregation-diffusion equations for collective behaviour in the sciences},
	author={Bailo, Rafael and Carrillo, José Antonio and Gómez-Castro, David},
	journal={Preprint arXiv: 2405.16679},
	year={2024},
	doi={10.48550/arXiv.2405.16679},
	archivePrefix={arXiv},
	arXivId={2405.16679},
	eprint={2405.16679},
}

This is a survey article based on the content of the plenary lecture given by José A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and applications of the vast area of aggregation-diffusion equations. We also discuss the implications in mathematical biology explaining cell sorting in tissue growth as an example of this modelling framework. This modelling strategy is quite successful in other timely applications such as global optimisation, parameter estimation and machine learning.

This is a survey article based on the content of the plenary lecture given by José A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and applications of the vast area of aggregation-diffusion equations. We also discuss the implications in mathematical biology explaining cell sorting in tissue growth as an example of this modelling framework. This modelling strategy is quite successful in other timely applications such as global optimisation, parameter estimation and machine learning.

header
Hello, world! This is a toast message.

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

arXiv: 2403.14470, 2024.

arXiv: 2403.14470, 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={Preprint arXiv: 2403.14470},
	year={2024},
	doi={10.48550/arXiv.2403.14470},
	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 optimization 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 optimization 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.

header
Hello, world! This is a toast message.

A finite-volume scheme for fractional diffusion on bounded domains

European Journal of Applied Mathematics, 2024 (to appear).

European Journal of Applied Mathematics, 2024 (to appear).

@Article{BCF2024
	title={A finite-volume scheme for fractional diffusion on bounded domains},
	author={Bailo, Rafael and Carrillo, José Antonio and Fronzoni, Stefano and Gómez-Castro, David},
	journal={European J. Appl. Math. (to appear)},
	year={2024},
	doi={10.48550/arXiv.2309.08283},
	archivePrefix={arXiv},
	arXivId={2309.08283},
	eprint={2309.08283},
}

We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the well-posedness theory for the fractional heat equation. We also develop a numerical scheme, which correctly captures the action of the fractional Laplacian and its anomalous diffusion effect. We benchmark numerical solutions for the L'evy-Fokker-Planck equation against known analytical solutions. We conclude by numerically exploring properties of these equations with respect to their stationary states and long-time asymptotics.

We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the well-posedness theory for the fractional heat equation. We also develop a numerical scheme, which correctly captures the action of the fractional Laplacian and its anomalous diffusion effect. We benchmark numerical solutions for the L'evy-Fokker-Planck equation against known analytical solutions. We conclude by numerically exploring properties of these equations with respect to their stationary states and long-time asymptotics.