Related papers: Uncertainty Quantification of Nonlinear Lagrangian…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters…
Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of…
In this work we investigate the nonlinear and nonlocal relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the recon- struction of the nonlinear velocity field from the fully nonlinear…
Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…
Adsorption is a relevant process in many fields, such as product manufacturing or pollution remediation in porous materials. Adsorption takes place at the molecular scale, amenable to be modeled by Lagrangian numerical methods. We have…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this,…
In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate…
The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…
Lagrangian Particle Tracking (LPT) enables practitioners to study various concepts in turbulence by measuring particle positions in flows of interest. This data is subject to measurement errors, and filtering techniques are applied to…
Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…
Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching…
In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…
The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e.,…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…