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In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…

The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…

We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find…

The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is…

This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization…

Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of…

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…

By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…

Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an…

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…

Precipitation nowcasting is a critical spatio-temporal prediction task for society to prevent severe damage owing to extreme weather events. Despite the advances in this field, the complex and stochastic nature of this task still poses…

Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…

We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

Estimation and counterfactual analysis in dynamic structural models rely on assumptions about the dynamic process of latent variables, which may be misspecified. We propose a framework to quantify the sensitivity of scalar parameters of…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…