Related papers: An Efficient and Statistically Accurate Lagrangian…

In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a…

In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the…

The implementation of intelligent transportation systems (ITS) has enhanced data collection in urban transportation through advanced traffic sensing devices. However, the high costs associated with installation and maintenance result in…

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Accurate and efficient global ocean state estimation remains a grand challenge for Earth system science, hindered by the dual bottlenecks of computational scalability and degraded data fidelity in traditional data assimilation (DA) and deep…

This paper considers a Leray regularization model of incompressible, non-isothermal fluid flows which uses nonlinear filtering based on indicator functions, and introduces an efficient numerical method for solving it. The proposed method…

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…

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…

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…

Lagrangian averaging has been shown to be more effective than Eulerian mean in separating waves from slow dynamics in two-timescale flows. It also appears in many reduced models that capture the wave feedback on the slow flow. Its…

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis…

We describe the application of a new technique from nonlinear dynamical systems to infer the Lagrangian connectivity of the deep global ocean. We approximate the dynamic Laplacian using Argo trajectories from January 2011 to January 2017…

Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We…

Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…