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Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…

Laplacian eigenvectors capture natural community structures on graphs and are widely used in spectral clustering and manifold learning. The use of Laplacian eigenvectors as embeddings for the purpose of multiscale graph comparison has…

A novel dynamically varying search radius algorithm is developed that takes advantage of bathymetry information to choose satellite observations that represent coastal sea level variability better. The algorithm is successfully tested at…

Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…

Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that…

Explicit filters play a pivotal role in the scale separation and numerical stability of advanced Large Eddy Simulation (LES) closures, such as dynamic eddy-viscosity or Approximate Deconvolution (AD) methods. In the present study, it is…

In a previous article a characteristic discontinuous Galerkin (CDG) advection scheme was presented for tracer transport. The scheme is conservative, unconditionally stable with respect to time step and scales sub-linearly with the number of…

We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…

Polarization calibration of interferometric observations is a costly procedure and, in some cases (e.g., a limited coverage of parallactic angle for the calibrator), it may not be possible to be performed. To avoid this worst-case scenario…

Moving objects leave extended tracks in optical images acquired with a telescope that is tracking stars or other targets. By searching images for these tracks, one can obtain statistics on populations of space debris in Earth orbit. The…

Trajectory anomaly detection underpins applications from fraud detection to urban mobility analysis. Dense GPS methods preserve fine-grained evidence such as abnormal speeds and short-duration events, but their quadratic cost makes…

We address Lagrangian drift simulation in geophysical dynamics and explore deep learning approaches to overcome known limitations of state-of-the-art model-based and Markovian approaches in terms of computational complexity and error…

We identify materially defined regions in unsteady two-dimensional flows that combine finite-time contraction with elevated accumulated intrinsic rotation along trajectories, which we term \emph{Lagrangian rotating contracting structures}…

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…

High Reynolds Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are…

Developing an effective evaluation metric is crucial for accurately and swiftly measuring LiDAR perception performance. One major issue is the lack of metrics that can simultaneously generate fast and accurate evaluations based on either…

Sea ice dynamics are crucial to the global climate system, yet traditional continuum (e.g., viscous-plastic) models often fail to represent the discrete floe interactions that dominate in the marginal ice zone. Lagrangian discrete element…

Graph anomaly detection (GAD), which aims to detect outliers in graph-structured data, has received increasing research attention recently. However, existing GAD methods assume identical training and testing distributions, which is rarely…