About
I am a theoretical physicist working on the statistical physics of disordered systems. I study how systems of many interacting units (spins, algorithms, epidemics, opinions, species) evolve in time when they live on sparse random graphs, and I develop local, cavity-based approximations that make this dynamics tractable.
I am an Assistant Professor at the Faculty of Physics of the University of Havana, where I work in the Center for Complex Systems. I received my PhD from the University of Havana in 2024 under the supervision of Dr. Roberto Mulet. My thesis was awarded the prize for the best doctoral thesis in Natural Sciences in Cuba. From 2024 to 2026 I was a postdoctoral researcher at Sapienza University of Rome, in the Statistical Mechanics and Complexity group.
Citation data from Google Scholar, October 2026.
News
- Our project RISE: Reconstructing Interactions in Sparse Ecosystems, with M. Negri (CY Cergy Paris Université) and P. Valigi (University of Bath), was selected in the CNRS International Research Projects call. It runs from 2027 to 2029.
- I joined the Scientific Council of the University of Havana.
- Alejandro Castro Cabrera defended his Master's thesis on opinion dynamics with heterophobic interactions.
- Published: local equations for the generalized Lotka–Volterra model in SciPost Physics, and algorithmic thresholds in combinatorial optimization in Physical Review X.
- I finished my postdoc at Sapienza University of Rome and returned to the University of Havana.
- Published: local equations describe unreasonably efficient stochastic algorithms in random K-SAT in PNAS.
Research
Dynamics on sparse random graphs
Cavity master equations, local closures and dynamic cavity methods for continuous-time stochastic dynamics of discrete variables, including Ising models, epidemics and glassy relaxation.
Algorithms for hard optimization
Local equations that describe stochastic local-search algorithms in random K-SAT, algorithmic thresholds and their time scaling, belief propagation, and benchmarks for graph neural networks.
Theoretical ecology
The generalized Lotka–Volterra model on sparse, asymmetric interaction networks, using Local Fokker–Planck equations to infer species interactions from data.
Social and biological networks
Opinion dynamics and consensus formation under heterophobic interactions, and message-passing models of neural activity in C. elegans.
Projects
RISE: Reconstructing Interactions in Sparse Ecosystems
This is a collaboration between the LPTM at CY Cergy Paris Université (project leader Dr. Matteo Negri), the Department of Mathematical Sciences at the University of Bath (Dr. Pietro Valigi) and the Faculty of Physics of the University of Havana. We adapt Local Fokker–Planck equations, pseudo-likelihood learning and graph neural networks to infer sparse, asymmetric interactions in ecosystems, both from synthetic data and from experimental data. The project funds researcher and student mobility, and a postgraduate student from Havana will be co-supervised in Havana and Paris.
When deep learning is not enough
The project's full title is "When deep learning is not enough: creating hard benchmarks and physics-inspired algorithms for combinatorial optimization problems." It was hosted at Sapienza University of Rome.
Publications
An up-to-date list with citation counts is on Google Scholar. † marks a student I supervised.
- Benchmarking graph neural networks in solving hard constraint satisfaction problemspreprint
G. Skenderi, L. Buffoni, F. D'Amico, D. Machado, R. Marino, M. Negri, F. Ricci-Tersenghi, C. Lucibello, M. C. Angelini
arXiv:2602.18419 (2026) - Belief propagation with informed initialization in combinatorial optimization problems
D. Machado, R. Mulet, A. Pérez
Revista Cubana de Física 43(1), 4–12 (2026) - Local equations for the generalized Lotka–Volterra model on sparse asymmetric graphs
D. Machado, P. Valigi, T. Tonolo, M. C. Angelini
SciPost Physics 21, 008 (2026) · arXiv - Algorithmic thresholds in combinatorial optimization depend on the time scaling
M. C. Angelini, M. Avila-González†, F. D'Amico, D. Machado, R. Mulet, F. Ricci-Tersenghi
Physical Review X 16, 011045 (2026) - Local equations describe unreasonably efficient stochastic algorithms in random K-SAT
D. Machado, J. González-García, R. Mulet
Proceedings of the National Academy of Sciences 122(49), e2510153122 (2025) - Heterophobic interactions hinder consensus formation in sparse random networks
A. Castro†, T. M. Pham, E. Ortega, D. Machado
Physical Review E 112, 064309 (2025) - Dynamic cavity method in fully-asymmetric models
J. González-García, D. Machado
Revista Cubana de Física 42(1), 12–19 (2025) - Improved mean-field dynamical equations are able to detect the two-step relaxation in glassy dynamics at low temperatures
D. Machado, R. Mulet, F. Ricci-Tersenghi
Journal of Statistical Mechanics: Theory and Experiment 2023, 123301 (2023) - A closure for the master equation starting from the dynamic cavity method
E. Aurell, D. Machado, R. Mulet
Journal of Physics A: Mathematical and Theoretical 56, 17LT02 (2023) - Modeling the neural activity of Caenorhabditis elegans through neural message passing
Y. Hernández-Hernández†, D. Machado, R. Mulet
Revista Cubana de Física 40(1), 39 (2023) - Dynamics of epidemics from cavity master equations: susceptible-infectious-susceptible models
E. Ortega, D. Machado, A. Lage-Castellanos
Physical Review E 105, 024308 (2022) - From random point processes to hierarchical cavity master equations for stochastic dynamics of disordered systems in random graphs: Ising models and epidemics
D. Machado, R. Mulet
Physical Review E 104, 054303 (2021) - The cavity master equation: average and fixed point of the ferromagnetic model in random graphs
E. Domínguez, D. Machado, R. Mulet
Journal of Statistical Mechanics: Theory and Experiment 2020, 073304 (2020) - Theory of non-equilibrium local search on random satisfaction problems
E. Aurell, E. Domínguez, D. Machado, R. Mulet
Physical Review Letters 123, 230602 (2019) - Exploring the diluted ferromagnetic p-spin model with a cavity master equation
E. Aurell, E. Domínguez, D. Machado, R. Mulet
Physical Review E 97, 050103(R) (2018)
Teaching & students
Courses
Current (2026–27): Differential Equations; Complex Variables.
Previously: Analytic Geometry, Algebra, Mathematical Analysis, Ordinary Differential Equations, and Mathematical Methods of Physics II (second-order PDEs). In 2020–21 the students voted me best professor of the Faculty.
Fisica Computazionale
I taught the laboratory sessions of the Computational Physics course in each of the two academic years of my postdoc.
Theses supervised
- Alejandro Castro CabreraM.Sc. · 2026
Opinion dynamics on random graphs: heterophobic interactions and the viability of consensus. The results were published in Phys. Rev. E. - Martín Avila GonzálezM.Sc. · 2026 · co-supervised with R. Mulet
Algorithmic thresholds in the random K-SAT ensemble: Simulated Annealing as a function of the time scaling. The results were published in Phys. Rev. X. - Martín Avila GonzálezLicenciatura · 2023 · co-supervised with R. Mulet
Modeling local-search algorithms for K-SAT: Simulated Annealing and WalkSAT. - Yeslaine Hernández HernándezLicenciatura · 2022 · co-supervised with R. Mulet
Modeling the neural activity of C. elegans with message-passing algorithms. The results were published in Rev. Cubana Fís.
Prospective students
I am looking for motivated Licenciatura and Master's students at the University of Havana who are interested in statistical physics, algorithms or theoretical ecology. RISE includes a postgraduate position with research stays in Paris. Write to me with a short note about your interests.
Selected talks
- International School on Statistical Inference from Biological Data, University of Havana (oral contribution)
- STATPHYS29, the 29th International Conference on Statistical Physics, Florence (oral contribution)
- Seminar at Sapienza University of Rome: "Approximate master equations for algorithmic dynamics in hard combinatorial optimization"
- Workshop "Towards a theory for typical-case algorithmic hardness", Les Houches (short talk and poster)
- 3rd International School of the Italian Society of Statistical Physics, Catania (flash talk)
- Seminar at the Complexity Science Hub, Vienna: "Two approximate approaches to the continuous-time dynamics of discrete variables in random graphs"
- Seminar at Sapienza University of Rome: "Dynamic cavity method for the continuous time: Ising models, epidemics and local-search algorithms"
- Seminar at NORDITA, Stockholm: "Cavity master equation applied to the diluted ferromagnetic p-spin"
Service & awards
Service
- Member of the Scientific Council of the University of Havana (since 2026)
- Substitute member of the Scientific Council of the Faculty of Physics
- Referee for Physical Review E, Physical Review Research and Revista Cubana de Física
Selected awards
- Award of the Cuban National Academy of Sciences (2025)
- Best Doctoral Thesis in Natural Sciences in Cuba, Ministry of Higher Education (2024)
- Distinguished Young Professor and Researcher, University of Havana (2024)
- Golden Diploma, top of the class, University of Havana (2019)