Related papers: Conditional Score-Based Modeling of Effective Lang…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…

Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative…

We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…

In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…

We consider the setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…

We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event…

Score-based diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which…

We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements of the system are feasible. Our method predicts the asymptotic behavior…

We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…