pierfrancesco urbani

Pierfrancesco Urbani

CNRS Researcher

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

+33 1 69 08 79 28
+33 1 69 08 81 20
pierfrancesco.urbani (at) ipht.fr

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

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. The main result is that it has allowed to obtain a new phase diagram of glasses at low temperature which 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.

Recently I also got more interested in the application of glass physics ideas to high dimensional optimization problems. Here I mainly focused on the study of minimization algorithms and their properties in a quite extended set of problems, going from high-dimensional inference problems, to learning in simple neural networks.

Main research activities and results

Solution of structural glass models in infinite dimension:

Gardner transition in structural glasses: mean field theory, RG analysis and experiments.
Theory of the Jamming transition: computation of the critical exponents and characterization of marginal stability; jamming of non-spherical particles, upper critical dimension and hyperuniformity. Jamming critical phase in linear soft spheres. Avalanches. Rigidity transition in confluent tissues.
Theory of the low temperature harmonic excitations of amorphous solids. Euclidean Random Matrices, Boson Peak and localized soft excitations.
Theory of two level system excitations.
Microscopic theory of rheology of amorphous solids: yielding as a critical spinodal with emerging RFIM criticality, shear-jamming of stable hard sphere glasses, two-step yielding, stability map of glasses, breakdown of elasticity at low temperatures.
Dynamical Criticality: computation of the dynamical critical exponents at the MCT transition as well as at the Gardner point.
Quasi-equilibrium approach to the dynamics of structural glasses.

Constraint satisfaction and optimization problems

Jamming in multilayer neural networks.
Emergence of isostatic marginally stable critical phases both in infinite and finite dimensional optimization problems. Theory of the corresponding non-linear excitations.
Dynamical mean field theory for gradient-based optimization.

High-dimensional statistical inference and machine learning

Glassy nature of the hard phase of inference problems.
Emergence of a generic gap between gradient based algorithms and message passing ones.
Analysis of gradient descent dynamics in high-dimensional inference problems. Momentum-based minimization algorithms.
Dynamical mean field theory for stochastic gradient descent. Persistent-SGD. Effective temperature.
Replica-symmetry-breaking implementation of Approximate Message Passing algorithms.

Field theory and renormalization

Field theory for the glass transition. Dynamical heterogeneities at the glass transition.
Non-perturbative renormalization group approach to instantons.
Field theory for soft anharmonic spin glasses in a field.
Scenario for the spin glass transition in a field: appearance of finite density of non-linear excitations.

Disordered high dimensional optimal control

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Publications

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

Google Scholars , Arxiv

Lectures

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)

Conferences/seminars/News