1,721,054 research outputs found
Uncertainty quantification and data assimilation – computational challenges in large-scale geoscience models
No full textAssessing and reducing the uncertainty of large-scale simulations
in the geosciences have become fundamental to increase
the reliability of model forecasts. One of the major challenges
arises when the description of model uncertainty and the availability
of field observations are not straightforward. Especially
in these cases, it is necessary to develop robust assimilation
approaches combined with computationally efficient procedures.
For instance, the use of appropriate surrogate models
and the implementation on emerging computing architectures
can help reduce the computational burden, provided that
the most significant non-linearities of the physical system
are preserved. This mini-symposium aims to discuss recent
advances in geoscience applications where parameter and
state estimation problems are tackled. Contributions dealing
with novel algorithmic approaches and efficient computational
procedures used in challenging applications are welcom
Scalable in Time Algorithms for Large Scale Predictive Science
No full textWe address the design and development of innovative
mathematical models for Predictive Science simulations
described by Variational Data Assimilation (DA) methods
tightly coupled with time-dependent Partial Differential
Equations (PDEs). The result is a PDE-based variational
problem that is extremely large scale. The innovation
refers to the simultaneous introduction of space-andtime
decomposition approaches, consisting of Parallel in
Time (PinT)-based approaches for solving the PDEs and
functional decomposition for solving the Variational DA
model; finally, domain is decomposed both along the space
and the time dimension. The core of our approach is that
the DA model acts as coarse-propagator/predictor for local
PDEs, by providing the background values for the local initial
conditions. The main outcome of this approach is that,
in contrast to other PinT-based approaches, local solvers
run concurrently, so that the resulting algorithm only requires
exchange of boundary conditions between adjacent
sub-domains. This work is carried on in collaboration with
E. Constantinescu (ANL) and L. Carracciuolo (CNR-IT)
A note on domain decomposition approaches for solving 3D variational data assimilation models
No full textData 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 (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a big and computationally expensive problem. In the present work we prove that the functional decomposition of the 3D variational data assimilation (3D Var DA) operator, previously introduced by the authors, is equivalent to apply multiplicative parallel Schwarz (MPS) method, to the Euler–Lagrange equations arising from the minimization of the data assimilation functional. It results that convergence issues as well as mesh refininement techniques and coarse grid correction—issues of the functional decomposition not previously addressed—could be employed to improve performance and scalability of the 3D Var DA functional decomposition in real cases
Model Reduction in space and time for ab initio decomposition of 4D Variational Data Assimilation problems
No full textWe present an innovative approach for solving time dependent Four Dimensional Variational Data Assimilation (4D VAR DA) problems. The proposed approach performs a decomposition of the whole physical domain, i.e. both along spatial and temporal directions; a reduction in space and time of both the Partial Differential Equations-based model and the Data Assimilation functional; finally it uses a modified regularization functional describing restricted 4D VAR DA problems on the domain decomposition. Innovation mainly lies in the introduction ab initio, i.e. on the numerical model – of a domain decomposition approach in space and time joining the idea of Schwarz's method and Parallel in Time (PinT)–based approaches. We provide the numerical framework of this method including convergence analysis and error propagation. A validation analysis is performed discussing computational results on a case study relying on Shallow Water Equations. © 2020 IMAC
Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case
No full textWe are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters n (i.e. the number of terms of Gaver’s formula) and δ (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by −┌log10 (δ)┐ + 1. In case of noise free data this number is arbitrarily large, as it is bounded below by n. We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach
A scalable Kalman Filter algorihm: trustworthy analysis on constrained least square model
No full textKalman filter (KF) is one of the most important and common estimation algorithms. We introduce an innovative designing of Kalman filter algorithm based on domain decomposition (we call it DD‐KF). DD‐KF involves decomposition of the whole computational problem, partitioning of the solution and a slight modification of KF algorithm allowing a correction at run‐time of local solutions. The resulted parallel algorithm consists of concurrent copies of KF algorithm, each one requiring the same amount of computations on each subdomain and an exchange of boundary conditions between adjacent subdomains. Main advantage of this approach is that it can be potentially applied in a moderately nonintrusive manner to existing codes for tracking and controlling systems in location, navigation, in computer graphics and in much more state estimation problems. To highlight the capability of DD‐KF of exploiting the computing power provided by future designs of microprocessors based on multi/many‐cores CPU/GPU technologies, we consider DD both at physical core level and at microprocessor level and we discuss scalability of DD‐KF algorithm at coarse and fine grained level. Throughout the present work, we derive and discuss DD‐KF algorithm for solving constrained least square model, which underlies any data sampling and estimation problem
A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation
Full text linkWe address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University
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