I'm a research associate at the University of Oxford, affiliated with the Oxford Centre for Nonlinear Partial Differential Equations at the Mathematical Institute. In addition, I have served as a non-stipendiary lecturer at the Queen's College and as a tutor at Magdalen College.

Prior to this, I 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.

In June 2024 I will be moving to the Centre for Analysis, Scientific Computing and Applications at TU/e as an assistant professor.

My primary area of interest lies in the numerical analysis of kinetic equations and other partial differential equations (PDEs). I'm also fascinated by collective dynamics, self-organisation, and the control of agent-based models.

Recent Publications

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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.

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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.

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Pedestrian models with congestion effects

Mathematical Models and Methods in Applied Sciences, 2024 (to appear).

Mathematical Models and Methods in Applied Sciences, 2024 (to appear).

@Article{ABD2024
	title={Pedestrian models with congestion effects},
	author={Aceves-Sánchez, Pedro and Bailo, Rafael and Degond, Pierre and Mercier, Zoé},
	journal={Math Models Methods Appl Sci (to appear)},
	year={2024},
	doi={10.1142/S0218202524400050},
	archivePrefix={arXiv},
	arXivId={2401.08630},
	halId={hal-04334055},
	eprint={2401.08630},
}

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behaviour. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw-Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behaviour. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw-Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.