Abstract: We often observe time series from complex, high-dimensional systems and seek models that are useful beyond short-term prediction. In many cases, reproducing individual trajectories is neither feasible nor meaningful—for instance, under partial observation, chaotic dynamics, or multiscale variability. Instead, the goal is to match a targeted set of statistical observables. Standard approaches enforce this by repeatedly simulating candidate models inside an iterative calibration loop, which can be prohibitively expensive in high dimensions.

In this talk, I will present two complementary directions that use information about target statistical features to construct and calibrate dynamical models while substantially reducing the number of required model integrations. The key enabling element is the score function—the gradient of the log steady-state probability density—which recent breakthroughs in score-based generative modeling have made tractable to estimate even from high-dimensional data. First, I show how integrating learned scores with the generalized fluctuation–dissipation theorem yields linear sensitivity information directly from unperturbed data, providing principled guidance for parameter updates while sharply reducing the number of required model runs. Second, I describe a stochastic reduced-modeling framework that starts from selected statistical observables—the steady-state distribution, together with time correlation constraints—and constructs surrogate dynamics that match these targets by design, while retaining explicit degrees of freedom to capture additional dynamical structure without sacrificing the enforced statistical features.

I will illustrate both directions on problems motivated by geophysical fluid dynamics, and discuss how the underlying ideas extend to climate dynamics, turbulent engineering flows, and nonequilibrium soft/active matter—along with implications for data-driven calibration and control.