Analysis of the Data Assimilation Methods from the Mathematical Point of View

2016 ◽  
pp. 193-205
Author(s):  
Tamás Szentimrey
Keyword(s):  
Data Assimilation ◽  
Point Of View ◽  
Mathematical Point

scholarly journals Contact interactions in complex fibrous metamaterials

2021 ◽  
Author(s):  
Mario Spagnuolo ◽  
Antonio M. Cazzani
Keyword(s):  
Strain Energy ◽  
Point Of View ◽  
The Other ◽  
Contact Interactions ◽  
Coupling Term ◽  
Dissipation Potential ◽  
Parallel Fibers ◽  
Mathematical Point

AbstractIn this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

scholarly journals Generalizations of the Lagrange mean value theorem and applications

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Miodrag Mateljevic ◽  
Marek Svetlik ◽  
Miloljub Albijanic ◽  
Nebojsa Savic
Keyword(s):  
Economic Growth ◽  
Growth Model ◽  
Arbitrary Function ◽  
Mean Value ◽  
Point Of View ◽  
Neoclassical Economic ◽  
Mean Value Theorem ◽  
Mathematical Point ◽  
Economic Growth Model

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

Jointly learning variational data assimilation models and solvers for geophysical dynamics

2021 ◽  
Author(s):  
Ronan Fablet ◽  
Bertrand Chapron ◽  
Lucas Drumetz ◽  
Etienne Memin ◽  
Olivier Pannekoucke ◽  
...  
Keyword(s):  
Neural Networks ◽  
Data Assimilation ◽  
Inverse Problems ◽  
Automatic Differentiation ◽  
Variational Data Assimilation ◽  
Point Of View ◽  
Variational Model ◽  
Short Term ◽  
End To End ◽  
Short Term Forecasting

<p>This paper addresses representation learning for the resolution of inverse problems  with geophysical dynamics. Among others, examples of inverse problems of interest include space-time interpolation, short-term forecasting, conditional simulation w.r.t. available observations, downscaling problems… From a methodological point of view, we rely on a variational data assimilation framework. Data assimilation (DA) aims to reconstruct the time evolution of some state given a series of  observations, possibly noisy and irregularly-sampled. Here, we investigate DA from a machine learning point of view backed by an underlying variational representation.  Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for variational data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the neural networks models using both supervised and unsupervised strategies. We first illustrate applications to the reconstruction of Lorenz-63 and Lorenz-96 systems from partial and noisy observations. Whereas the gain issued from the supervised learning setting emphasizes the relevance of groundtruthed observation dataset for real-world case-studies, these results also suggest new means to design data assimilation models from data. Especially, they suggest that learning task-oriented representations of the underlying dynamics may be beneficial. We further discuss applications to short-term forecasting and sampling design along with preliminary results for the reconstruction of sea surface currents from satellite altimetry data. </p><p>This abstract is supported by a preprint available online: https://arxiv.org/abs/2007.12941</p>

S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

Games of Chance: I. The Banker’s Clock

1933 ◽  
Vol 17 (226) ◽  
pp. 296-297
Author(s):  
S.T Shovelton
Keyword(s):  
Point Of View ◽  
Mathematical Point ◽  
Mathematical Probability ◽  
Games Of Chance ◽  
The Face

The game of Banker’s Clock provides an interesting question in mathematical probability In this game the banker turns up in sequence the first twelve cards of a well-shuffled ordinary pack of 52 cards. He backs himself to turn up at least one card of which the face value corresponds to its position in the sequence, an Ace ranking as one, a Jack as eleven and a Queen as twelve. The interest in the question from the mathematical point of view is in finding the probability that the event will happen.

Note on the FFT Based Computational Code and Its Application

2008 ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Toeplitz Matrix ◽  
Contact Problems ◽  
Point Of View ◽  
Fast Fourier Transform Algorithm ◽  
Discrete Convolution ◽  
Mathematical Point ◽  
Computational Code

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.

A Kind of Enhanced Slotted ALOHA Algorithm for Anti-Collision in RFID System

2013 ◽  
Vol 756-759 ◽  
pp. 3497-3500
Author(s):  
Fan Wei Meng ◽  
Yue Zhao ◽  
Cui Hong Ma ◽  
You Liang Yang
Keyword(s):  
Real Time ◽  
System Performance ◽  
Conflict Situation ◽  
Point Of View ◽  
Slotted Aloha ◽  
Mathematical Point ◽  
Frame Length ◽  
Time Estimates ◽  
Rfid System ◽  
Framed Slotted Aloha

in the RFID system, the conflict caused by the multi-label has been affecting system performance. This paper proposed a grouping dynamic framed slotted ALOHA algorithm based on the analysis of ALOHA algorithm. According to the conflict situation, to make real-time estimates the number of tags on the dynamic framed slotted ALOHA algorithm from the mathematical point of view, Dynamically change the frame length or the labels are grouped to reduce the label probability of collisions, thereby improving the efficiency of the recognition.

scholarly journals Ensemble Kalman Filtering with a Divided State-Space Strategy for Coupled Data Assimilation Problems*

2014 ◽  
Vol 142 (12) ◽  
pp. 4542-4558 ◽  
Author(s):  
Xiaodong Luo ◽  
Ibrahim Hoteit
Keyword(s):  
Data Assimilation ◽  
State Space ◽  
Point Of View ◽  
Coupled Systems ◽  
Current Status ◽  
Estimation Strategy ◽  
Coupled Subsystems ◽  
Coupled Data Assimilation ◽  
Augmented State ◽  
Lorenz 96

Abstract This study considers the data assimilation problem in coupled systems, which consists of two components (subsystems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the subsystems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. This work presents a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual subsystem, involving quantities from the subsystem itself and correlated quantities from other coupled subsystems. On top of the divided state-space estimation strategy, the authors also consider the possibility of running the subsystems separately. Combining these two ideas, a few variants of the EnKF are derived. The introduction of these variants is mainly inspired by the current status and challenges in coupled data assimilation problems and thus might be of interest from a practical point of view. Numerical experiments with a multiscale Lorenz 96 model are conducted to evaluate the performance of these variants against that of the conventional EnKF. In addition, specific for coupled data assimilation problems, two prototypes of extensions of the presented methods are also developed in order to achieve a trade-off between efficiency and accuracy.

On the initial conditions of the ICON-D2-EPS ensemble: An analysis in terms of spread and skill.

2020 ◽  
Author(s):  
Chiara Marsigli
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Weather Forecast ◽  
Point Of View ◽  
Ensemble Forecasting ◽  
Limited Area ◽  
Initial Condition ◽  
Weather Situation ◽  
Operational Phase ◽  
Data Assimilation System

<p><span>The COSMO-D2-EPS ensemble is running operationally at DWD at a resolution of 2.2 km. In the framework of the transition from the COSMO to the ICON model for the limited-area applications, the ICON-D2-EPS ensemble is starting its pre-operational phase. Therefore, the perturbation strategy developed for COSMO-D2-EPS is adapted to the new ensemble.</span><br><span>In this work, the focus is on the initial conditions, which are provided by the first 20 analyses generated by a LETKF ensemble data assimilation system (KENDA).</span><br><span>The KENDA analyses present the advantage of providing perturbed initial conditions to the convection-permitting ensemble, where the perturbations contain also the information on the convection-permitting scale uncertainties. On the other hand, the KENDA analyses are optimised for </span><span>the purpose of data assimilation. The ensemble of analyses which is the most suitable for initialising the next data assimilation cycle may not be the same which is the most suitable for initialising the weather forecast ensemble, e.g. in terms of spread.</span></p><p><span>The analyses generated by the KENDA cycle are evaluated from the point of view of their usage for ensemble forecasting initialisation. Their spread is computed for different variables, assessing also how it varies with the spatial scale and with the weather situation. Furthermore, the spread is compared to the error of the analyses and of the forecasts, in order to assess the ability of the analyses to describe the initial condition uncertainty. </span><br><span>The growth of the differences between the members during the first hours of the forecasts is studied as well, in dependence on the weather situation.</span></p><p><span>The final aim of this work is to identify possible improvements for deriving the ensemble initial conditions from the KENDA analyses.</span></p>

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