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Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
There has been great progress in improving numerical weather prediction and climate models using machine learning. However, most global models act at a kilometer-scale, making it challenging to model individual clouds and factors such as…
In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of…
Methods to deal with systematic model errors are an increasingly important component of modern data assimilation systems and their effectiveness has increased in recent years thanks to advances in methodology and the quality and density of…
In order to better comprehend the global carbon cycle and predict the prognosis for the response to climate change, accurate assessment of sea-air CO2 flux is necessary. Comparing to the relative homogeneously distribution of atmospheric…
High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…
4D millimeter-wave (mmWave) radars are sensors that provide robustness against adverse weather conditions (rain, snow, fog, etc.), and as such they are increasingly used for odometry and SLAM (Simultaneous Location and Mapping). However,…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
Data-driven machine learning (ML) models are reshaping weather forecasting and have shown the potential to accelerate and surpass traditional physics-based approaches, leading to a second revolution in the field after data assimilation.…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting…
In this paper, we introduce an end-to-end framework for video analysis focused towards practical scenarios built on theoretical foundations from sparse representation, including a novel descriptor for general purpose video analysis. In our…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational…
We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
The ability to predict wind is crucial for both energy production and weather forecasting. Mechanistic models that form the basis of traditional forecasting perform poorly near the ground. In this paper, we take an alternative data-driven…