Luca Leuzzi

Johannes Lang, Vincenzo Citro, Luca Leuzzi et al.

Understanding the dynamics of systems evolving in complex and rugged energy landscapes is central across physics, economics, biology, and computer science. Disordered mean-field models provide a powerful framework, as exact Dynamical Mean-Field Equations (DMFE) can be derived. However, solving the DMFE -- a set of coupled integral-differential equations for two-time functions -- remains a major numerical challenge. So far, large-time solutions of DMFE rely either on analytical approaches, such as the Cugliandolo--Kurchan ansatz based on assumptions like weak ergodicity breaking (which is known to fail in some cases), or on numerical integrations that reliably reach times $O(10^3)$ and extend further only via poorly controlled approximations. Consequently, no general method currently exists to solve DMFE at very long times, limiting the study of slow dynamics in complex landscapes. We present \textsc{Dynamite} (DYNAmical Mean-fIeld Time Evolution solver), a high-performance framework for solving DMFE up to unprecedented times $t=O(10^7)$. It combines non-uniform interpolation, adaptive time stepping, and numerical `renormalization' of memory, enabling accurate evaluation of history integrals. Its asymptotic runtime is linear, with sublinear memory scaling. Stability and precision are ensured via an adaptive Runge--Kutta scheme and periodic sparsification of the past. \textsc{Dynamite} achieves orders-of-magnitude speedups over uniform-grid methods while maintaining accuracy and reproducibility on CPU and GPU architectures. Benchmarks on glassy mean-field models, including the mixed spherical $p$-spin system, demonstrate access to aging and relaxation regimes previously out of reach. The framework provides a reproducible and extensible foundation for studying long-memory dynamical systems.

Daniele Ancora, Luca Leuzzi

One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing control or reconstructing images in complex media. In the present work, we investigate how statistical inference helps the calculation of the transmission matrix in a complex scrambling environment, enabling its usage like a normal optical element. We convert a linear input-output transmission problem into a statistical formulation based on pseudolikelihood maximization, learning the coupling matrix via random sampling of intensity realizations. Our aim is to uncover insights from the scattering problem, encouraging the development of novel imaging techniques for better medical investigations, borrowing a number of statistical tools from spin-glass theory.

Daniele Ancora, Luca Leuzzi

Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that can focus or transmit an image through disorder. Here, converting an input-output problem into a statistical mechanical formulation, we investigate how inference protocols can learn the transmission couplings by pseudolikelihood maximization. Bridging linear regression and thermodynamics let us propose an innovative framework to pursue the solution of the scattering-riddle.