Ludovico Theo Giorgini

My collaborators and I have developed a practical response-theoretic framework for predicting how nonlinear, high-dimensional systems respond to weak perturbations from observations of their unperturbed dynamics. The generalized fluctuation–dissipation theorem (GFDT) expresses this response through time-correlation functions, but its implementation requires the stationary score. Estimating the score accurately in high dimensions has been a principal computational obstacle to applying the GFDT beyond idealized settings. We have combined modern score-matching methods with the GFDT and validated the resulting response estimates on nonlinear stochastic PDEs. More recently, we extended this framework to statistical parameter calibration by interpreting infinitesimal changes in drift and diffusion parameters as dynamical perturbations. The resulting formulas express the sensitivities of stationary observables to all model parameters as time-correlation integrals evaluated along unperturbed trajectories; these sensitivities can then guide parameter updates that bring model statistics toward prescribed targets using only a few model integrations. For lower-dimensional systems, we also developed KGMM, a clustering-based method for accurate and computationally efficient score estimation. Building on these advances, we are using GFDT response sensitivities to identify low-dimensional, target-dependent parameter subspaces for calibrating high-dimensional models.

Representative work: Giorgini et al. (2024), Giorgini, Falasca, and Souza (2025), Giorgini, Bischoff, and Souza (2025), and Giorgini, Bischoff, and Souza (2026).

Many systems in the physical sciences and engineering couple nonlinear processes across widely separated spatial and temporal scales. The quantities of scientific interest, however, often depend only on a much smaller set of coarse observables and their statistics rather than on the complete high-dimensional state. The goal is therefore to use coarse data from observations, experiments, or high-fidelity simulations to construct efficient stochastic models that evolve only these resolved variables while reproducing the statistical and dynamical observables of interest. The difficulty is that the dynamics of the coarse variables are generally not closed: unresolved degrees of freedom influence their evolution through effective dissipation, fluctuations, feedback, and memory. I construct Markovian a priori closures directly from the statistical and finite-time dynamical observables they must reproduce. Instead of specifying a local evolution law and then testing its long-time behavior, the construction begins with these target observables and asks which stochastic models reproduce them by construction. The stationary score—the gradient of the logarithm of the steady-state probability density—characterizes a broad class of stochastic models that preserve the observed distribution by construction; combining it with linear response theory through the generalized fluctuation–dissipation theorem provides complementary dynamical constraints that restrict this class to models reproducing selected finite-time observables. The admissible family is therefore determined directly from observable constraints, without repeated simulations of candidate closures.

Representative work: Giorgini (2026), Giorgini, Bischoff, and Souza (2025), Giorgini (2026), and Del Felice and Giorgini (2026).