Pierfrancesco Urbani

CNRS Researcher

Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France

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email.gif pierfrancesco.urbani (at) ipht.fr

I am a statistical physicist working on disordered and glassy systems and on their applications to optimization, inference and learning problems.

My two main lines of research are: the physics of amorphous solids and high dimensional optimization problems, from learning to inference.

For what concerns structural glasses, my activity has focused on the construction of a theory of the glass phase starting from the soluble yet non-perturbative limit of infinite dimensions. This has allowed the characterization of the complete phase diagram of glasses. At low temperature, this analysis has shown the emergence of the so-called Gardner phase in which amorphous solids are marginally stable against external perturbations. This phase is the potential missing ingredient to unify the physics of anomalies of low temperature glasses and a large part of my recent activity has gone in this direction. The consequences of this discovery are already well established for colloidal-like glasses where we have shown that the Gardner phase is crucial for the computation of the critical exponent of the jamming transition and jamming-critical systems. My activity now focuses on the understanding of how marginal stability associated to the Gardner phase gives rise to non-linear excitations in amorphous solids. These excitations are typically postulated in phenomenological approaches to the rheology of amorphous solids. My main goal is to understand their dynamical generation from microscopic interactions and to uncover their collective nature and statistical properties.

I also work in high dimensional optimization problems. My main focus has been the study of optimization algorithms and their properties in a set of applications, going from high-dimensional inference problems, to learning in simple neural networks. In high-dimensional statistical inference I have analyzed of the posterior measure of prototypical models first suggesting that reconstruction algorithms based on message passing could have been more effective than gradient based algorithms due to glassy phases. Then I focused on the study of gradient based algorithms first suggesting that the landscape trivialization transition is not a necessary condition for having good performances which has important consequences for learning problems where absence of spurious minima have been advocated to explain good performances. More recently my main activity has been the analysis of the main workhorse algorithm in deep learning which is stochastic gradient descent. I used dynamical mean field theory to analyze of this algorithm in simple yet prototypical cases and I have shown that SGD can outperform gradient descent in hard high-dimensional learning problems.

More recently I started a research line at the crossroad of statistical physics and theoretical neuroscience

Here below there is a list of the main results obtained.

Main research activities and results

Solution of structural glass models in infinite dimension:

Constraint satisfaction and optimization problems

High-dimensional statistical inference and machine learning

Learning in Recurrent Neural Networks

Field theory and renormalization

Disordered high dimensional optimal control


G. Parisi, P. Urbani, F. Zamponi. Theory of simple glasses. Cambridge University Press 2020.

Google Scholars , Arxiv



IPhT Lectures on disordered and glassy systems (video)

Les Houches Lectures on dynamics in high dimension (2020) (lecture 1, lecture 2, lecture 3)

Lectures at the School on Disordered Elastic Systems, São Paulo, Brazil, 2022 (Lecture 1, Lecture 2, Lecture 3, Lecture 4)

IPhT Lectures: Generative models in a nutshell, upcoming in May 2024





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