arXiv subjects

Ludovico T. Giorgini

Publications and source records attributed to Ludovico T. Giorgini.

7 recordsLinked to original sources

arXiv2026

Stochastic coupling of climate variables and ice volume over the Late Pleistocene glacial cycles

Understanding the interactions between ice sheets and global climate forcings over geological timescales is essential for projecting their future. Previous studies have highlighted the role of ice dynamics and climate interactions in establishing the 100,000-year glacial cycles, particularly regarding the growth of the North American ice sheet. Researchers have reconstructed consistent time series for ice volume, temperature, and carbon dioxide by applying inverse forward modeling to benthic oxygen isotope records. Here we model the stochastic behavior of paleoclimate time series to evaluate the coupling between climate variables during the Pleistocene glacial cycles. We quantify the behavior of these time series using multifractal time-weighted detrended fluctuation analysis, which differentiates between near-red-noise and white-noise behavior below and above the 100,000-year glacial cycle, respectively, in all records. This study builds upon the work of Keyes et al. [Chaos vol. 33, 093132 (2023)] by incorporating ice volume into a five-variable model that includes carbon dioxide, methane, nitrous oxide, and temperature, along with intervariable coupling terms to capture potential relationships among these variables. Our analysis shows that ice volume, carbon dioxide, and temperature have a stabilizing effect upon each other. To test our model, we compute response functions for each pair of variables and compare these with empirical data, confirming our predictions regarding intervariable stability and coupling. This study provides a comprehensive overview of glacial-interglacial dynamics and highlights the role of cryosphere-climate feedbacks in shaping Earth's climate evolution.

physics.ao-ph↗

arXiv2026

Conditional Score-Based Modeling of Effective Langevin Dynamics

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simulation of candidate models, which become unreliable or computationally expensive for high-dimensional systems, coarse temporal sampling, or unevenly sampled data. We introduce a data-driven calibration method based on a novel relationship between the coefficients of a stochastic reduced model and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The resulting identity expresses derivatives of lagged correlation functions as stationary expectations over observed lagged pairs involving this conditional score and the unknown model coefficients. This formulation allows the drift and diffusion structure to be constrained directly from finite-lag statistics, without differentiating trajectories, partitioning state space, or repeatedly integrating candidate reduced models during calibration, yielding a least-squares fitting problem over stationary lagged pairs. We validate the approach on three systems of increasing complexity: an analytically tractable Cox--Ingersoll--Ross diffusion, a two-dimensional nonequilibrium diffusion with affine multiplicative noise, and a periodic soft-spin stochastic Landau--Lifshitz chain. Across these tests, the inferred models preserve the invariant statistics while reproducing finite-lag dynamical correlations. The framework provides a scalable route for learning stochastic reduced-order models from data that reproduce prescribed statistical and dynamical properties.

stat.ML↗

arXiv2026

Statistical Parameter Calibration via the Generalized Fluctuation Dissipation Theorem and Generative Modeling

We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with respect to drift and diffusion parameters admits an exact linear-response representation as a time-correlation integral evaluated along unperturbed dynamics alone, without perturbed simulations, adjoint derivations, or tangent-linear models. The key idea is to interpret infinitesimal parameter variations as causal perturbations of the dynamics, thereby bringing the Generalized Fluctuation-Dissipation Theorem to inverse problems. The resulting kernels couple observables to the score of the invariant density, for which modern score-estimation methods provide practical non-Gaussian estimators. We validate the framework across a hierarchy of models, from analytically tractable processes to stochastic parameterization in the chaotic Lorenz-96 system, and show that a single baseline trajectory can recover parameter sensitivities and calibration updates with accuracy comparable to finite-difference approaches. More broadly, the framework opens a new route to model calibration, statistical inverse problems, and uncertainty quantification when the quantities of interest are long-time statistics of complex dynamical systems.

nlin.CD↗

arXiv2025

KGMM: A K-means Clustering Approach to Gaussian Mixture Modeling for Score Function Estimation

We propose a hybrid method for accurately estimating the score function, i.e., the gradient of the log steady-state density, using a Gaussian Mixture Model (GMM) in conjunction with a bisecting K-means clustering step. Our approach, which we call KGMM, offers a systematic way to combine statistical density estimation with a neural-network-based interpolation of the score, leveraging the strengths of both. We demonstrate its ability to accurately reconstruct the long-time statistical properties of several paradigmatic systems, including potential systems, chaotic Lorenz-type models, and the Kuramoto-Sivashinsky equation. Numerical experiments show that KGMM yields robust estimates of the score function, even for small values of the covariance amplitude in the GMM, where standard GMM methods tend to fail because of noise amplification. We compare the performance of KGMM against the conventional Denoising Score Matching (DSM) approach, demonstrating that KGMM achieves more faithful reconstruction of the steady-state distribution for low-dimensional systems at a fraction of the computational cost. These accurate estimates allow us to build effective stochastic reduced-order models that reproduce the invariant measures of the target dynamics.

nlin.CD↗

arXiv2025

Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling

We present a novel and flexible data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation--Dissipation Theorem (GFDT) links the unperturbed steady-state distribution to the system's linear response. While standard implementations relying on Gaussian approximations can predict the mean response, they often fail to capture changes in higher-order moments. To overcome this, we combine GFDT with score-based generative modeling to estimate the system's score function directly from data. We demonstrate the framework's versatility by employing two complementary score estimation techniques tailored to the system's characteristics: (i) a clustering-based algorithm (KGMM) for systems with low-dimensional effective dynamics, and (ii) a denoising score matching method implemented with a U-Net architecture for high-dimensional, spatially-extended systems where reduced-order modeling is not feasible. Our method is validated on several stochastic models relevant to climate dynamics: three reduced-order models of increasing complexity and a 2D Navier--Stokes model representing a turbulent flow with a localized perturbation. In all cases, the approach accurately captures strongly nonlinear and non-Gaussian features of the system's response, significantly outperforming traditional Gaussian approximations.

stat.ML↗

arXiv2024

Instantons in $ϕ^4$ Theories: Transseries, Virial Theorems and Numerical Aspects

We discuss numerical aspects of instantons in two- and three-dimensional $ϕ^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $ϕ^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations.

hep-th↗

arXiv2021

Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, and the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the $O(1)$, $O(2)$, and $O(3)$ oscillators, and demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior.

hep-th↗