Related papers: Continuous data assimilation for two-phase flow: a…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often only time-averaged data is available, which poses challenges for DA in the context of unsteady flow…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized…
In this paper, we propose, analyze, and test a new fully discrete, efficient, decoupled, stable, and practically second-order time-stepping algorithm for computing MHD ensemble flow averages under uncertainties in the initial conditions and…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we…
We present a positivity-preserving method for multi-resolution simulations of compressible flows involving extreme conditions such as near vacuum and strong discontinuities. The novelty of this work is due to two aspects. First we extend…
Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-B\'{e}nard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
Dataset distillation seeks to synthesize a highly compact dataset that achieves performance comparable to the original dataset on downstream tasks. For the classification task that use pre-trained self-supervised models as backbones,…
The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…
In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…
We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…
Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input…
Time-lapse seismic data acquisition is an essential tool to monitor changes in a reservoir due to fluid injection, such as CO$_2$ injection. By acquiring multiple seismic surveys in the exact location, we can identify the reservoir changes…
Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…