Related papers: Data Assimilation: A Mathematical Introduction
A framework for data assimilation combining aspects of operator-theoretic ergodic theory and quantum mechanics is developed. This framework adapts the Dirac--von Neumann formalism of quantum dynamics and measurement to perform sequential…
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
The popularity of deep learning has led to the curation of a vast number of massive and multifarious datasets. Despite having close-to-human performance on individual tasks, training parameter-hungry models on large datasets poses…
Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…
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…
This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this…
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…
This is a survey of old and new problems and results in additive number theory.
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
The widespread use of machine learning and data-driven algorithms for decision making has been steadily increasing over many years. \emph{Bias} in the data can adversely affect this decision-making. We present a new mitigation strategy to…
This chapter amalgamates some foundational developments and calculations in factorization homology.
A review of the superstatistics concept is provided, including various recent applications to complex systems.
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…