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Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth…
In Microscopic Particle Image Velocimetry ($\mu$PIV), velocity fields in microchannels are sampled over finite volumes within which the velocity fields themselves may vary significantly. In the past, this has limited measurements often to…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
Time series data from a variety of sensors and IoT devices need effective compression to reduce storage and I/O bandwidth requirements. While most time series databases and systems rely on lossless compression, lossy techniques offer even…
In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity…
We propose a 3D meshless method to compute mean pressure fields in turbulent flows from image velocimetry. The method is an extension of the constrained Radial Basis Function (RBF) formulation by \citet{Sperotto2022} to a Reynolds Averaged…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using…
In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our new strategy is based on the classical Milstein method from stochastic differential…
In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion…
Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from sparse and noisy particle tracks obtained…
Time-resolved measurements of quantum dynamics are based on the availability of controlled events (e.g. pump and probe pulses) that are shorter in duration than the typical evolution time scale of the dynamical processes to be observed.…
We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…
Measuring stress fields in fluids and soft materials is crucial in various fields such as mechanical engineering, medicine, and bioengineering. However, conventional methods that calculate stress fields from velocity fields struggle to…
The compressible Navier-Stokes-Poisson system takes the form of usual Navier-Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electric field of…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…