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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A real-time variational data assimilation method with data-driven model enrichment for time-dependent problems
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A real-time variational data assimilation method with data-driven model enrichment for time-dependent problems

机译：A real-time variational data assimilation method with data-driven model enrichment for time-dependent problems

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We propose an extension of the Parameterized-Background-Data-Weak (PBDW) formulation, introduced in Maday et al. (2015), to the time-dependent context for state reconstruction and prediction-in-time purposes. This method provides a non -intrusive, real-time, and in-situ data assimilation framework for physical systems modeled by parameterized Partial Differential Equations. Given a sequential set of M measurements at acquisition time tk, the key idea of the proposed formulation is to seek an approximation ukN,M = zkN,M + eta kN,M of the true state uktr ue employing projection-by-data; the first term comes from a background estimate zkN,M computed from a reduced-basis N-dimensional linear space informed by the parameterized mathematical model, while the second term comes from an update state eta kN,M informed by experimental observations (hybrid modeling with correction of model bias). The contributions of this work are twofold. First, we present a new formulation adapted to time-dependent parameterized problems of the classical PBDW strategy. In particular, the N-dimensional linear space is here constructed using a space/time/parameter decomposition. Furthermore, we exploit the evolution features to enrich the biased model with previous updates, and to extrapolate in time the estimated states in order to predict and monitor the physical system. We set up and analyze a synthetic numerical example of thermal diffusion with different biases to assess and compare performance of three formulations of the proposed approach.(c) 2022 Elsevier B.V. All rights reserved.

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