arXiv subjects

Ludovico Theo Giorgini

Publications and source records attributed to Ludovico Theo Giorgini.

7 recordsLinked to original sources

arXiv2026

Score-based stochastic reduced-order models of barotropic quasi-geostrophic turbulence

In many turbulent flows, the quantities of interest are coarse-grained variables, either because resolving the fine scales is computationally prohibitive or because only coarse observations are available; in both cases, data-driven reduced-order models that evolve only these variables are required. Even when the governing equations are known, their projection onto the coarse variables is not closed, and the central difficulty lies in representing the feedback of the unresolved scales so that the reduced model reproduces the statistical and dynamical properties of the projected high-resolution system. We address this problem with a score-based framework, constructing a reduced-order model of quasi-geostrophic turbulence whose stationary distribution coincides by construction with the distribution learned from data and whose dynamics are calibrated to reproduce the finite-time correlations of the energies in individual wavenumber shells. The resulting model reproduces the stationary statistics of the resolved flow with high accuracy, and its calibration is computationally inexpensive because it requires no forward integration of the model.

nlin.CD↗

arXiv2026

Score-Based Modeling of Effective Langevin Dynamics

We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed steady-state density \emph{by design} and enforces short-lag coordinate-correlation constraints directly from data -- so that the surrogate satisfies the targeted invariant measure and short-lag coordinate-correlation constraints from the outset, without trial-and-error tuning. The drift is parameterized in terms of the score function -- the gradient of the logarithm of the steady-state distribution -- and a constant mobility matrix whose symmetric part controls dissipation and diffusion and whose antisymmetric part encodes mean nonequilibrium circulation. The score is learned from samples using denoising score matching, while the mobility coefficients are inferred from short-lag correlation identities estimated via a clustering-based finite-volume discretization on a data-adaptive state-space partition. We validate the approach on low-dimensional stochastic benchmarks and on partially observed Kuramoto--Sivashinsky dynamics, where the resulting Markovian surrogate preserves the marginal invariant measure and captures the temporal correlations of the resolved modes. The resulting Langevin models define explicit reduced generators that enable efficient sampling and generation of synthetic trajectories with the imposed statistical and dynamical constraints, without direct simulation of the underlying full dynamics.

nlin.CD↗

arXiv2025

Integrating Score-Based Generative Modeling and Neural ODEs for Accurate Representation of Multiscale Chaotic Dynamics

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term statistical properties governed by slow variables and the short-term transient dynamics driven by fast chaotic processes. We present a hybrid data-driven framework that integrates score-based generative modeling with Neural Ordinary Differential Equations (NODEs) to construct reduced-order models (ROMs) capable of reproducing both regimes. The slow dynamics are represented by a Langevin equation whose drift is informed by a score function learned via the K-means Gaussian Mixture Model (KGMM) method, ensuring faithful reproduction of the system's invariant measure. The fast chaotic forcing is modeled by a NODE trained on delay-embedded residuals extracted from observed trajectories, replacing conventional Gaussian noise approximations. We validate this approach on a hierarchy of prototypical metastable systems driven by Lorenz 63 dynamics, including bistable potentials with additive and multiplicative forcing, and tristable non-autonomous systems with cycloperiodic components. Our results demonstrate that the hybrid framework maintains statistical consistency over long time horizons while accurately forecasting rare critical transitions between metastable states with lead times approaching the Lyapunov time of the chaotic driver. This work establishes a principled methodology for combining statistical closure techniques with explicit surrogate models of fast dynamics, offering a pathway toward predictive modeling of complex multiscale phenomena where both long-term statistics and short-term transients are essential.

nlin.CD↗

arXiv2025

Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods

Many natural systems exhibit cyclo-stationary behavior characterized by periodic forcing such as annual and diurnal cycles. We present a data-driven method leveraging recent advances in score-based generative modeling to construct reduced-order models for such cyclo-stationary time series. Our approach accurately reproduces the statistical properties and temporal correlations of the original data, enabling efficient generation of synthetic trajectories. We demonstrate the performance of the method through application to the Planet Simulator (PlaSim) climate model, constructing a reduced-order model for the 20 leading principal components of surface temperature driven by the annual cycle. The resulting surrogate model accurately reproduces the marginal and joint probability distributions, autocorrelation functions, and spatial coherence of the original climate system across multiple validation metrics. The approach offers substantial computational advantages, enabling generation of centuries of synthetic climate data in minutes compared to weeks required for equivalent full model simulations. This work opens new possibilities for efficient modeling of periodically forced systems across diverse scientific domains, providing a principled framework for balancing computational efficiency with physical fidelity in reduced-order modeling applications.

nlin.CD↗

arXiv2024

Response Theory via Generative Score Modeling

We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics. We numerically validate our approach using time-series data from three different stochastic partial differential equations of increasing complexity: an Ornstein-Uhlenbeck process with spatially correlated noise, a modified stochastic Allen-Cahn equation, and the 2D Navier-Stokes equations. We demonstrate the improved accuracy of the methodology over conventional methods and discuss its potential as a versatile tool for predicting the statistical behavior of complex dynamical systems.

physics.data-an↗

arXiv2024

Reduced Markovian Models of Dynamical Systems

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of timescales. We demonstrate the methodology on three low-dimensional dynamical systems with stochastic and chaotic dynamics. We then apply the method to two high-dimensional dynamical systems, the Kuramoto-Sivashinky equations and data sampled from fluid-flow experiments via Particle-Image Velocimetry. We show that the methodology presented herein provides a robust reduced-order statistical representation of the underlying system.

nlin.CD↗

arXiv2020

Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.

physics.comp-ph↗