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Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the…

Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…

We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to…

We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on…

Are there hidden dynamical common patterns in the evolution of social and cultural history? While the growing availability of digitized social data invites us to answer this question, prevailing quantitative methods often rely on…

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…

This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…

Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the…