2019年度第8回 AIMR数学連携グループセミナー

 

日時:2019年12月11日(水)14:00~15:00
場所:AIMR本館 3C 3C区画内ミーティングスペース

 

Speaker: Yves Antonio Brandes Costa Barbosa

Title: Data Assimilation and Uncertainty Quantification in Partial Differential Equations

 

Abstract

Data Assimilation (DA) [2] is a process for integrating the knowledge provided by numerical models and measurements with the purpose of improving the overall reliability of the quantita tive analysis. This approach has been developed since the mid of the twentieth century and have been vastly studied in the context of weather forecasting. The rationale behind DA is that the predictions provided by numerical models, i.e. background knowledge, are mainly based on universal physical and onstitutive laws, but in real-world problems are often affected by numerous

sources of uncertainties [3]. The causes of uncertainty range from the nature of the simplifying assumptions taken as hypothesis of the problem up to the incomplete knowledge of parameters,

usually needed by the constitutive laws to define the athematical model. Therefore, the integration of traditional modelling with available measurements, i.e. foreground knowledge, that

incapsulate the nuances of the specific features of the case under investigation, is paramount in the construction of reliable models. On one hand, it is beneficial to the quantitative analysis, since we are able to reduce the uncertainty in the mathematical models. On the other hand, the background information improves the knowledge extracted from the data, providing a way for filtering noise.
In this perspective, DA reduces possibilities of failure in estimating, predicting, and identifying the state and/or the parameters of a specific system by merging background and foreground information in a unique quantitative analysis. The necessity of this process in the traditional development of numerical models became more urgent with the substantial increase in the access to data and, more importantly, with the increase in the number of applications that need to incorporate this data in their analysis via a cost-effective and accurate algorithm.
The goal of this presentation is to provide a broad introduction to the subject, exemplifying how to incoporate uncertain data in conventional analysis, and to show the overall benefits of the

various DA methods. The focus will be on how to apply DA techniques in the numerical solution of ordinary differential equations and partial differential equations, applications that suffer from substatial limitations in the assessment of uncertainty due to the computational burden associated with their solutions. In particular, the DA analysis will be illustrated in applications arising from Computational Fluid Dynamics (CFD), such as the Advection-Diffusion-Reaction problem [1].


 

 

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