arXiv subjects

Raffaele Marino

Publications and source records attributed to Raffaele Marino.

At least 19 recordsLinked to original sources

arXiv2026

Multiplicity of Stable Attractors in Disordered Neural Models

We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.

cond-mat.dis-nn↗

arXiv2026

Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes

In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted attractors serve as indicators for the target classes, while the velocity field leveraging the universal approximation capabilities of the architecture shapes the dynamical landscape. This process defines the basins of attraction of the trained model, effectively directing each input (provided as an initial condition) toward its corresponding destination target.

cond-mat.dis-nn↗

arXiv2026

Scaling laws and local enhancements of buoyancy flux in stratified turbulent flows

In the presence of stratification, turbulent flows exhibit intermittency not only at small scales but also at large scales, comparable to the mean flow, as observed in the atmosphere and oceans. We study such flows through a large parametric exploration using direct numerical simulations of the Boussinesq equations with different forcing types. We examine two Prandtl numbers (1 and 6) and vary the Froude number ($Fr$) over a range of geophysical interest values, $0.01\le Fr \le 1$, corresponding to a variation in terms of the buoyancy Reynolds number ($R_{IB}$) of $0.06\le R_{IB} \le 2300$. We analyze the dependence on $R_{IB}$ of the buoyancy flux ($B_f$), the mixing efficiency, the shear parameters, and the vertical momentum flux. Strongly non-Gaussian tails in the spatio-temporal distribution of the $B_f$ are observed, with kurtosis reaching $\approx 10^2$, indicating the potential for stratified geophysical flows to be characterized by highly variable transport properties along the direction of gravity even under stable stratification. This is associated with long-time intermittent behavior of vertical velocity and temperature at large scale, which produces local turbulence and enhances dissipation and transport. We present evidence that the skewness of $B_f$ increases with $R_{IB}$ as a power-law and saturates in the passive-scalar limit. We also show that the domain-averaged $B_f$ exhibits two distinct trends: logarithmic growth with $R_{IB}$ and approach to a small offset as stratification strengthens. A simple model for the temporal evolution of energy and $B_f$ indicates that the defect between vertical and potential energy drives strong $B_f$ events. This trend directly leads to convective instabilities, the formation of two-dimensional and three-dimensional eddies, and rapid dissipation on a turnover timescale, allowing the energetic cycle to restart-also occurring in bursts.

physics.flu-dyn↗

arXiv2026

Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

cond-mat.dis-nn↗

arXiv2026

Helicity subgrid-scale models and their numerical validation

Large-eddy simulations (LES) with an appropriate subgrid-scale (SGS) model provide a powerful tool for investigating real-world turbulence. The Smagorinsky model, one of the simplest and most used SGS models, often shows an over-dissipative behavior even when using dynamic procedures to adjust the model coefficient. By incorporating the structural or geometrical information of turbulence provided by helicity (velocity-vorticity correlations), the helicity SGS model is expected to alleviate these issues in the standard Smagorinsky framework, in which only information of turbulence intensity is considered through the turbulent energy. The validity of helicity SGS models is investigated here with the aid of direct numerical simulations (DNSs). Using configurations with and without net rotation, and with large-scale helicity gradients sustained by a mechanical forcing, we show that to better model SGS turbulence, SGS helicity effects should be incorporated into the model together with the Smagorinsky-like eddy viscosity.

physics.flu-dyn↗

arXiv2026

Benchmarking Graph Neural Networks in Solving Hard Constraint Satisfaction Problems

Graph neural networks (GNNs) are increasingly applied to hard optimization problems, often claiming superiority over classical heuristics. However, such claims risk being unsolid due to a lack of standard benchmarks on truly hard instances. From a statistical physics perspective, we propose new hard benchmarks based on random problems. We provide these benchmarks, along with performance results from both classical heuristics and GNNs. Our fair comparison shows that classical algorithms still outperform GNNs. We discuss the challenges for neural networks in this domain. Future claims of superiority can be made more robust using our benchmarks, available at https://github.com/ArtLabBocconi/RandCSPBench.

cond-mat.dis-nn↗

arXiv2026

Smart Walkers in Discrete Space

We study the statistical properties of trainable agents moving in discrete space. After introducing the mathematical framework, we first analyze the dynamics of two completely random walkers, mutually competing in a chaser-target interaction scheme. The statistics of the encounters is analytically obtained and the predictions tested versus numerical simulations. We then move forward to extend the baseline case to agents capable of learning and adapting to an external reward signal, using reinforcement learning. Smart walkers morph the statistics of the encounter, to maximize their cumulated reward, as confirmed by combined numerical and analytical insights. More interestingly, configuration entropy proves a reliable proxy to gauge the acquired ability of the agents to cope with the assigned task when no other information about them (i.e. reward signal, policy, etc) is present. We further test the proposed measure of learned skills by operating the Stockfish chess engine against a quasi-random untrained opponent. The obtained conclusions corroborate our claim. Summing up, our primary contribution is to propose and test a quantitative measure of agents' awareness that naturally correlates with the inherent complexity of the task being performed.

cond-mat.stat-mech↗

arXiv2025

Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach

In machine learning practice it is often useful to identify relevant input features. Isolating key input elements, ranked according their respective degree of relevance, can help to elaborate on the process of decision making. Here, we propose a novel method to estimate the relative importance of the input components for a Deep Neural Network. This is achieved by leveraging on a spectral re-parametrization of the optimization process. Eigenvalues associated to input nodes provide in fact a robust proxy to gauge the relevance of the supplied entry features. Notably, the spectral features ranking is performed automatically, as a byproduct of the network training, with no additional processing to be carried out. Moreover, by leveraging on the regularization of the eigenvalues, it is possible to enforce solutions making use of a minimum subset of the input components, increasing the explainability of the model and providing sparse input representations. The technique is compared to the most common methods in the literature and is successfully challenged against both synthetic and real data.

cs.LG↗

arXiv2025

Train Stochastic Non Linear Coupled ODEs to Classify and Generate

A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, point attractors are turned into probability distributions, made analytically accessible via the linear noise approximation. The addition of noise proves beneficial to oppose adversarial attacks, a property that gets engraved into the trained adjacency matrix and therefore also inherited by the deterministic counterpart of the optimized stochastic model. By providing samples from the target distribution as an input to a feedforward neural network (or even to a dynamical model of the same typology of the adopted for classification purposes), yields a fully generative scheme. Conditional generation is also possible by merging classification and generation modalities. Automatic disentanglement of isolated key features is finally proven.

cond-mat.dis-nn↗

arXiv2025

Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows

The dispersion of Lagrangian particle pairs is a fundamental process in turbulence, with implications for mixing, transport, and the statistical properties of particles in geophysical and environmental flows. While classical theories describe pair dispersion through scaling laws related to energy cascades, extreme events in turbulent flows can significantly alter these dynamics. This is especially important in stratified flows, where intermittency manifests itself also as strong updrafts and downdrafts. In this study, we investigate the influence of extreme events on the relative dispersion of particle pairs in stably stratified turbulence. Using numerical simulations we analyze the statistical properties of pair separation across different regimes, and quantify deviations from classical Richardson scaling. Our results highlight the role of extreme drafts in accelerating dispersion. These findings have important implications for turbulent mixing in natural systems, including atmospheric and oceanic flows, as well as applications in cloud microphysics and pollutant transport.

physics.flu-dyn↗

arXiv2025

Energy cascades in rotating and stratified turbulence in anisotropic domains

The concept of inverse energy cascades has played a central role in the development of turbulence theory, with applications in two-dimensional and quasi-two-dimensional flows. We examine the presence or absence of inverse energy cascades in rotating stably stratified flows constrained to anisotropic yet fully three-dimensional domains, in a range of parameters that are relevant for planetary atmospheres. In particular, we focus on regimes with aspect ratios, Rossby, and Froude numbers similar to those found in the Earth's and other planets atmospheres. Our results show that, under certain conditions, inverse energy cascades can indeed emerge from the dry fluid dynamics solely, suggesting that this process can play a role in intermediate-scale atmospheric self-organization processes.

physics.flu-dyn↗

arXiv2025

Characterization of local energy transfer in large-scale intermittent stratified turbulent flows via coarse graining

Recent studies based on simulations of the Boussinesq equations indicate that stratified turbulent flows can develop large-scale intermittency in the velocity and temperature fields, as detected in the atmosphere and oceans. In particular, emerging powerful vertical drafts were found to generate local turbulence, proving necessary for stratified flows to dissipate the energy as efficiently as homogeneous isotropic turbulent flows. The existence of regions characterized by enhanced turbulence and dissipation, as observed, for instance, in the ocean, requires appropriate tools to assess how energy is transferred across the scales and at the same time locally in the physical space. After refining a classical space-filtering procedure, here we investigate the feedback of extreme vertical velocity drafts on energy transfer and exchanges in subdomains of simulations of stably stratified flows of geophysical interest. Our analysis shows that vertical drafts are indeed able to trigger upscale and downscale energy transfers, strengthening the coupling between kinetic and potential energies at certain scales, depending on the intensity of the local vertical velocity.

physics.flu-dyn↗

arXiv2024

Learning in Wilson-Cowan model for metapopulation

The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

q-bio.NC↗

arXiv2024

Large-scale self-organisation in dry turbulent atmospheres

How turbulent convective fluctuations organise to form large-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption that this process is the result of an inverse cascade was suggested half a century ago in two-dimensional fluids, but its applicability to atmospheric and oceanic flows remains heavily debated, hampering our understanding of the energy balance in planetary systems. We show with direct numerical simulations of spatial resolutions of 122882 $\times$ 384 points that rotating and stratified flows can support a bidirectional cascade of energy, in three dimensions, with a ratio of Rossby to Froude numbers comparable to that of the Earth's atmosphere. Our results establish that in dry atmospheres spontaneous order can arise via an inverse cascade to the largest spatial scales.

physics.flu-dyn↗

arXiv2024

Charging a quantum spin network towards Heisenberg-limited precision

We present a cooperative protocol to charge quantum spin networks up to the highest-energy configuration, in terms of the network's magnetization. The charging protocol leverages spin-spin interactions and the crossing of a phase transition's critical point. Exploiting collective dynamics of the spin network, the cooperative protocol guarantees a precision advantage over any local charging protocol and leads to fluctuations (standard deviation) of the magnetization that scale as $1/N$, with $N$ being the number of spins in the network, i.e., the size of the spin battery. These findings mirror the Heisenberg limit for precision for parameter estimation in quantum metrology. We test our protocol on the D-Wave's Advantage quantum processing unit by charging sub-lattices with sizes ranging from $40$ to $5\,612$ spins, achieving the maximum magnetization and reaching a scalable charging precision beyond the standard quantum limit of $1/\sqrt{N}$.

quant-ph↗

arXiv2024

Multi-Particle Dispersion in Rotating-Stratified Turbulent Flows

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably-stratified Boussinsesq equations, with Brunt-Väisälä frequency $N$ and Coriolis parameter $f$. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio $N/f = 5$. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backwards in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when $N$ and $f$ increase. We also find evidence for the formation of shear layers, which become more pronounced as $N$ and $f$ become larger. Finally, we show that the irreversibility on the dispersion of a set of particles forming initially a regular tetrahedron becomes weaker when the influence of stratification and rotation increase, a property that we relate to that of the perceived rate-of-strain tensor.

physics.flu-dyn↗

arXiv2024

Fast Analysis of the OpenAI O1-Preview Model in Solving Random K-SAT Problem: Does the LLM Solve the Problem Itself or Call an External SAT Solver?

In this manuscript, I present an analysis on the performance of OpenAI O1-preview model in solving random K-SAT instances for K$\in {2,3,4}$ as a function of $α=M/N$ where $M$ is the number of clauses and $N$ is the number of variables of the satisfiable problem. I show that the model can call an external SAT solver to solve the instances, rather than solving them directly. Despite using external solvers, the model reports incorrect assignments as output. Moreover, I propose and present an analysis to quantify whether the OpenAI O1-preview model demonstrates a spark of intelligence or merely makes random guesses when outputting an assignment for a Boolean satisfiability problem.

cs.CL↗

arXiv2024

Evidence of dual energy transfer driven by magnetic reconnection at sub-ion scales

The properties of energy transfer in the kinetic range of plasma turbulence have fundamental implications on the turbulent heating of space and astrophysical plasmas. It was recently suggested that magnetic reconnection may be responsible for driving the sub-ion scale cascade, and that this process would be characterized by a direct energy transfer towards even smaller scales (until dissipation), and a simultaneous inverse transfer of energy towards larger scales, until the ion break. Here we employ the space-filter technique on high-resolution 2D3V hybrid-Vlasov simulations of continuously driven turbulence providing for the first time quantitative evidence that magnetic reconnection is indeed able to trigger a dual energy transfer originating at sub-ion scales.

physics.plasm-ph↗