Related papers: Model discovery on the fly using continuous data a…

Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation…

We propose a novel learning-based surrogate data assimilation (DA) model for efficient state estimation in a limited area. Our model employs a feedforward neural network for online computation, eliminating the need for integrating…

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…

We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models,…

Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This…

We propose, analyze, and test a novel continuous data assimilation reduced order model (DA-ROM) for simulating incompressible flows. While ROMs have a long history of success on certain problems with recurring dominant structures, they tend…

Reconstructing accurate causal models of dynamic systems from time-series of sensor data is a key problem in many real-world scenarios. In this paper, we present an overview based on our experience about practical challenges that the causal…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain…

We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with…

In this paper we combine the non-linear filtering capabilities of particle filters with the transdimensional inference of the reversible-jump Markov chain Monte Carlo method for a data assimilation methodology over dynamic problems with…

Increasing the resolution of a model can improve the performance of a data assimilation system: first because model field are in better agreement with high resolution observations, then the corrections are better sustained and, with…

A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial…

Latent Dirichlet Allocation (LDA) is a popular topic modeling technique for exploring document collections. Because of the increasing prevalence of large datasets, there is a need to improve the scalability of inference of LDA. In this…

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…

The rapid rise of air pollution events necessitates accurate, real-time monitoring for informed mitigation strategies. Data Assimilation (DA) methods provide promising solutions, but their effectiveness hinges heavily on optimal measurement…

Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent…