Dates: from Sept. 1, 2026 to Aug. 31, 2029

Funder: Ministerio de Ciencia, Innovación y Universidades (Spain)

Project id: PID2025-176129NB-I00

Total Funding: 94,875€

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This proposal addresses fundamental problems at the interface of statistical physics, network science, and machine learning by developing new methodologies for learning generative models of network data. Current approaches face a fundamental limitation: deep learning-based generative models are powerful but often opaque, while probabilistic inference methods rooted in statistical physics are interpretable but constrained in expressiveness or scalability. The starting hypothesis is that combining both approaches will lead to more expressive generative network models, deeper understanding of network-generating mechanisms, and more efficient, well-grounded inference approaches.

The overarching goal is thus to develop statistical physics tools to learn generative models for networks by integrating probabilistic inference and graph representation learning into a unified methodological framework. The project focuses on two areas: (i) learning generative models from multiple observations of unlabeled graphs (network alignment), and (ii) learning generative models from graph embeddings.

For network alignment, the project aims to develop new probabilistic inference models capable of handling time-evolving networks, networks with different numbers of nodes, networks with node attributes, and networks alignable at the group level. The project will also establish rigorous statistical methods to assess alignment quality and model reliabilitycapabilities currently lacking in heuristic approaches. For graph embeddings, the project aims to develop embedding spaces that retain all information about collections of graphs and permit full reconstruction of network structure; and to model network evolution as continuous dynamical processes within these embedding spaces, using Bayesian symbolic regression to extract closed-form differential or stochastic equations describing how graphs change over time.

The methodology is unified by a statistical physics perspective that exploits the deep analogy between probabilistic inference and statistical mechanics. The posterior probability of a model given data can be expressed as a Boltzmann factor, enabling the use of statistical mechanics approaches to solve inference problems. This framework underlies probabilistic network inference, graph embedding methods that leverage diffusion processes, and Bayesian symbolic regression for discovering closed-form mathematical expressionsall formulated as network inference problems. Beyond proposed applications in neuroscience, molecular modeling, socioeconomic systems, and digital medicine, the results have potential to influence a wide range of fields where networks, inference, and generative modeling play a central role.