WPI-AIMR Math Unit

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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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AIMR数学連携グループハイブリッドセミナー

日程：2024年4月19日（金）
講演者：竹田航太

東北大学材料科学高等研究所｜数学連携グループ

▼研究内容 ▼メンバー ▼受賞・報道 ▼研究会・セミナー情報 ▼これまでの活動記録 ▼お知らせ ▼リンク ▼アクセス・お問い合わせ

2019年度第8回 AIMR数学連携グループセミナー

【新着情報】

　▼研究内容　▼メンバー　▼受賞・報道　▼研究会・セミナー情報　　▼これまでの活動記録　▼お知らせ　▼リンク　▼アクセス・お問い合わせ