Curriculum learning for data-driven modeling of dynamical systems.

The reliable prediction of the temporal behavior of complex systems is key in numerous scientific fields. This strong interest is however hindered by modeling issues: Often, the governing equations describing the physics of the system under consideration are not accessible or, when known, their solution might require a computational time incompatible with the prediction time constraints. Not surprisingly, approximating complex systems in a generic functional format and informing it ex-nihilo from available observations has become common practice in the age of machine learning, as illustrated by the numerous successful examples based on deep neural networks.

Constrained Reversible System for Navier-Stokes Turbulence.

Following a Gallavotti's conjecture, stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the Navier-Stokes equation itself. We discuss a model system symmetric under time reversal based on the Navier-Stokes equations constrained to keep the enstrophy constant. It is demonstrated through highly resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations (DNS) at different Reynolds numbers.

Wave-turbulence theory of four-wave nonlinear interactions.

The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of a generating function and of a multipoint probability density function (PDF), for weakly interacting waves with initial random phases. When the initial amplitudes are also random, a one-point PDF equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions.

Elastic wave turbulence and intermittency.

We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics.

Reaction spreading on percolating clusters.

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t)~t(d(l)), where d(l) is the connectivity dimension.

Front speed in reactive compressible stirred media.

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate.

Reaction spreading on graphs.

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e.

Mesoscopic lattice boltzmann modeling of flowing soft systems.

A mesoscopic multicomponent lattice Boltzmann model with short-range repulsion between different species and short (midranged) attractive (repulsive) interactions between like molecules is introduced. The interplay between these composite interactions gives rise to a rich configurational dynamics of the density field, exhibiting many features of disordered liquid dispersions (microemulsions) and soft-glassy materials, such as long-time relaxation due to caging effects, anomalous enhanced viscosity, aging effects under moderate shear and flow above a critical shear rate.