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Project information

Probabilistic modelling of complex systems with uncertainty: from molecules to human interactions

M. Castro J.L. Gómez J. Pérez

September 2023 - August 2026

Funding entity Ministerio de Ciencia de Innovación (MCI) / Agencia Estatal de Investigación (AEI)

Some of the most exciting phenomena that have aroused scientific curiosity in recent decades (such as genomics, the emergence of pandemics, the collaborative economy, or the immune response to a pathogen) are collective phenomena out of equilibrium and result from the interactions of simple basic units. In these systems converge (although to different degrees) a set of similar problems common to Complexity science: they occur at different scales (many of them unobservable), they cannot be explained by knowledge of the essential components, and, finally, they are fluctuating, and uncertainty cannot be controlled experimentally. Although many of these problems have already been successfully addressed in recent years, pursuing a unifying theory that is universally valid in all situations is unrealistic. While some patterns can be transferred from one field to another, it is imprecise to generalize from pure metaphor to the quantitative, systematic, and rigorous scientific analysis that characterizes physics. However, it is possible to unify the methodology by considering the specific knowledge of the problem. The novelty of this project is to focus on the universality of the probabilistic description of uncertainty to systematically model each problem using the language of probability. Specifically, using Bayes' Theorem to capture the particular mechanism and the evolution of uncertainty. In the case of physicochemical phenomena, this is reduced to the probabilistic inference of the model parameters. However, as microscopic knowledge of the problem becomes less detailed, the weight of probabilistic modeling becomes more important. In particular, we propose to study diverse systems, from the physics of vapor reservoirs (which gives rise to fractal surfaces) to the dynamics of a sharing economy system, where modeling is based on the maximum entropy principle to determine the variability of mobility patterns in a bike-sharing system, Other examples are epidemiology or immunology. We combine Langevin equations and Markov chains to, through stochasticity, integrate experimentally unobservable degrees of freedom, again described by probability distributions compatible with empirical evidence. In summary, we propose a theoretical framework with uncertainty at the heart of the problem. However, we illustrate it (in the absence of genuinely universal models) using examples from various disciplines. The project team has established expertise in these problems to achieve the project objectives. We also introduce machine learning methodology to analyze experimental data and use it to generate new hypotheses. The project's ultimate goal is to realize models that can help to contrast alternative hypotheses of a problem and help, with the help of experiments, to falsify those contradictory to them.

Layman's summary: In this project, we study complex phenomena from immunology to computational social sciences. Using probabilistic methods, we aim to create models that help analyze data in various fields, test hypotheses, and enhance the understanding of these phenomena.