An efficient SPDE approach for El Niño

Mena, Hermann; Pfurtscheller, Lena-Maria

doi:10.1016/j.amc.2019.01.071

Cited by 6 publications

(5 citation statements)

References 27 publications

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“…For analysing asymptotic properties of this estimator, it is crucial to investigate the correlation structure of quadratic temporal increments and the product of consecutive temporal increments, as evident by (21).…”

Section: Andmentioning

confidence: 99%

“…Therefore, it is intuitive that applications of these SPDEs is also of great relevance, especially for two-and three-dimensional spaces. See, for instance, [21] for an application in connection with the climate phenomenon El Niño and references therein for applications to sea temperature, [23] for an application in Geostatistics and dealing with seismic data and [10] for an application in climate science. For an overview with many references to specific applications in various fields we refer to [19].…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation for second-order SPDEs in multiple space dimensions

Bossert

2023

Preprint

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We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one and two spatial dimensions was established in recent literature, this is the first work which generalizes the theory to a general, multi-dimensional framework.Our approach builds upon realized volatilities, enabling the construction of an oracle estimator for volatility within the underlying model. Furthermore, we show that the realized volatilities have an asymptotic illustration as response of a log-linear model with spatial explanatory variable. This yields novel and efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. For proving central limit theorems, we use a high-frequency observation scheme. To showcase our results, we conduct a Monte Carlo simulation. MSC Classification: 62F12, 62M10, 60H15

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Section: Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parameter estimation for second-order SPDEs in multiple space dimensions

Bossert

2023

Preprint

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“…; see, e.g. [20,75], for applications. When matrices are large, it is important to exploit that applying the right hand side in (9.63) does not increase the rank of X(t) too much, which is guaranteed here, if J is not too large and the matrix C is of low rank.…”

Section: Matrix Equationsmentioning

confidence: 99%

Geometric Methods on Low-Rank Matrix and Tensor Manifolds

Uschmajew

Vandereycken

2020

Handbook of Variational Methods for Nonlinear Geometric Data

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In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors.

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“…This is characterized by an unusual warming of the sea surface temperature in the Indo-Pacific ocean. It can be modeled by https://www.nvidia.com/en-us/data-center/tesla-p100/ a stochastic advection equation driven by additive noise [38] and its covariance is given by a DLE of the form Ṗ (t) = AP (t) + P (t)A T + Q, see [34,35] for details. The matrix A arises from a centered finite difference approximation of the advection operator and Q is the discretized covariance operator of the random noise.…”

Section: Example 1: Heat Equation Random Modelmentioning

confidence: 99%

GPU acceleration of splitting schemes applied to differential matrix equations

2019

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We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.

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An efficient SPDE approach for El Niño

Cited by 6 publications

References 27 publications

Parameter estimation for second-order SPDEs in multiple space dimensions

Parameter estimation for second-order SPDEs in multiple space dimensions

Geometric Methods on Low-Rank Matrix and Tensor Manifolds

GPU acceleration of splitting schemes applied to differential matrix equations

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