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PubblicazioneLatent dynamics graph convolutional networks for model order reduction of parameterized time-dependent PDEs( 2026)Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding spatial information. In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN), a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned on external inputs and parameters. The temporal evolution is modeled in the latent space and advanced through time-stepping, allowing for time-extrapolation, and the trajectories are consistently decoded onto geometrically parameterized domains using a GNN. Our framework enhances interpretability by enabling the analysis of the reduced dynamics and supporting zero-shot prediction through latent interpolation. The methodology is mathematically validated via a universal approximation theorem for encoder-free architectures, and numerically tested on complex computational mechanics problems involving physical and geometric parameters, including the detection of bifurcating phenomena for Navier–Stokes equations.
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PubblicazioneStatistical Learning across Representational Levels: Neural and Behavioral Expression, Modality, Individual Variability and Lifespan(SISSA, 2026-06-25)Statistical learning (SL) refers to the ability to extract regularities from structured sensory input and has been proposed as a fundamental mechanism supporting language acquisition, reading, and adaptive behavior. Despite extensive research, important questions remain regarding the nature of SL, its organization across modalities, its development across the lifespan, and the relationship between neural and behavioral expressions of learning. The present thesis addressed these questions through a series of behavioral and imaging studies examining SL in children, young adults, and older adults. Across the empirical chapters, SL was investigated using both neural frequency-tagging paradigms and behavioral measures, with a particular focus on modality-specificity, cross-modal transfer, individual variability, and lifespan changes. Results revealed robust neural sensitivity to structured regularities in both young and older adults, even when explicit behavioral evidence of learning was weak or absent. Cross-modal studies further demonstrated that learning and transfer varied across auditory and visual domains, suggesting that SL is shaped by both shared computational principles and modality-specific representational constraints. Developmental and aging findings indicated that some forms of sensitivity to regularities remain relatively preserved across the lifespan, although the behavioral expression of learning and the integration of information across modalities may differ as a function of age. Across studies, substantial inter-individual variability emerged, and correlations between neural and behavioral measures were often limited. These findings challenge strongly unitary conceptions of SL and instead support the view that learning is best understood as a multicomponential phenomenon. Building on these results, the thesis proposes a multi-level framework in which different paradigms capture distinct expressions of learning that vary in representational format, processing demands, and accessibility to conscious report. Within this framework, neural entrainment primarily reflects early online sensitivity to statistical structure, whereas behavioral measures additionally recruit processes related to prediction, memory retrieval, decision-making, and metacognitive reflection. Overall, the present work argues that SL is neither fully domain-general nor entirely modality-specific, but rather emerges from dynamic interactions among perceptual systems, prior knowledge, developmental factors, and individual cognitive differences. By integrating neural and behavioral methodologies across modalities and age groups, the thesis contributes to a more comprehensive understanding of how humans acquire and generalize statistical structure in complex sensory environments.
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PubblicazioneNon-toric 5d SCFTs from Reid's Pagoda( 2025)We construct new families of non-toric 5d SCFTs via abelian orbifolds of the Reid Pagoda, including a surprising infinite family of rank-1 theories, that evade all known classifications. Using the McKay correspondence, we derive their BPS quivers and superpotentials. The hallmark of these theories is a novel sector we dub Pagoda matter, whose vacuum expectation values obstruct the Kähler moduli. This mechanism freezes the gauge coupling to infinite value, precluding a weak-coupling limit and rendering the theories intrinsically strongly coupled. Finally, we interpret these results as 5d SCFTs deformed by non-constant flavor backgrounds.
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PubblicazioneRandom Initial Data and Average Shock Time in the Fermi-Pasta-Ulam-Tsingou Chain( 2026)We investigate the dynamics of the Fermi-Pasta-Ulam-Tsingou chain with long-wavelength random initial data. When the energy per particle is small, thermal equilibrium is not reached on a fast timescale, and the system enters prethermalization. The formation of the prethermal state is characterized by the development of a Burgers-type shock and the onset of a turbulentlike spectrum with a time dependent exponent zeta(t) in the inertial range. We perform a significant step forward by demonstrating that these features are robust under generic long-wavelength random initial conditions. By employing advanced probabilistic techniques inspired by the works of Dudley and Talagrand, we derive a sharp asymptotic expression for the average shock time in the thermodynamic limit. For large p, this time scales as (p ffiffiffiffiffiffiffiffiffiffi plog p)-1, where p is the number of excited modes, proving that it is an intensive quantity up to a logarithmic correction in the size of the system.
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PubblicazioneEntanglement and Quantum Complexity in Monitored Quantum Many-Body Systems(SISSA, 2025-09-15)Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.