Ludovico Theo Giorgini | Applied Mathematics

About Me

I am an applied mathematician developing data-driven reduced-order models for complex multiscale systems. My research combines score-based generative modeling, stochastic dynamics, response theory, and neural differential equations to construct computationally efficient models that preserve observed statistics, temporal correlations, and responses to perturbations, with applications in fluid dynamics, geophysics, and statistical physics.

Research

Score-Based Stochastic Reduced-Order Models

Markovian closures that reproduce prescribed stationary distributions and dynamical correlations directly from data, without repeated solver-in-the-loop calibration.

Response Theory and Parameter Calibration

Generalized fluctuation-dissipation methods for predicting forced responses and estimating sensitivities of statistical observables from unperturbed trajectories.

Multiscale and Chaotic Dynamics

Hybrid Langevin and neural-ODE models that combine accurate long-time statistics with short-time prediction of rare transitions in multiscale systems.

Selected Publications

For the complete publication record, see Google Scholar.

L. T. Giorgini, Score-Based Modeling of Effective Langevin Dynamics, Physical Review E 114, L012102 (2026).
L. T. Giorgini, Conditional Score-Based Modeling of Effective Langevin Dynamics, arXiv:2604.23952 (2026).
G. Del Felice and L. T. Giorgini, Integrating Score-Based Generative Modeling and Neural ODEs for Accurate Representation of Multiscale Chaotic Dynamics, Chaos 36, 063143 (2026).
L. T. Giorgini, T. Bischoff, and A. N. Souza, Statistical Parameter Calibration with the Generalized Fluctuation-Dissipation Theorem and Generative Modeling, arXiv:2509.19660 (2025).
L. T. Giorgini, T. Bischoff, and A. N. Souza, Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods, arXiv:2508.19448 (2025).
L. T. Giorgini, F. Falasca, and A. N. Souza, Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling, Proceedings of the National Academy of Sciences 122, e2509578122 (2025).
L. T. Giorgini, T. Bischoff, and A. N. Souza, KGMM: A K-Means Clustering Approach to Gaussian Mixture Modeling for Score Function Estimation, arXiv:2503.18054 (2025).
L. T. Giorgini, K. Deck, T. Bischoff, and A. N. Souza, Response Theory via Generative Score Modeling, Physical Review Letters 133, 267302 (2024).

Open-Source Software

Featured Research Software

StateDependentMobility.jl

Tools for learning and validating state-dependent mobility tensors in effective Langevin models from finite-lag trajectory data and conditional scores.

Code Paper

ScoreUNet1D.jl

One-dimensional score U-Nets trained by denoising score matching, with Langevin validation for coarse-grained Kuramoto–Sivashinsky dynamics.

Code Paper

ScoreEstimation.jl

KGMM and neural interpolation for estimating score functions, divergences, and score Jacobians from high-dimensional samples.

Code Paper

ParameterCalibration.jl

GFDT conjugate observables, trajectory-based sensitivity matrices, and Newton-style updates for drift and diffusion parameters.

Code Paper

FastSDE.jl

A speed-first Julia library for stochastic and deterministic integration, including threaded ensembles and batched neural-network drift evaluation.

Code

Time-Series Forecasting

DiscreteTransformers.jl

Transformer forecasting on clustered state sequences, with ensemble generation and statistical validation of long synthetic trajectories.

Code

ContinuousTransformers.jl

Transformer forecasting directly on continuous-valued delay embeddings for next-step prediction, ensembles, and forecast-horizon analysis.

Code

Contact

Email: ludogio@mit.edu
Office: Room 2-165
Address: Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139