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A variational approach for parameter estimation based on balanced proper orthogonal decomposition

机译：基于平衡适当正交分解的变分参数估计方法

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The adjoint method has been used significantly for parameter estimation. This requires a significant programming effort to build adjoint model code and is computationally expensive as cost of one adjoint simulation often exceeds several original model runs. The work proposed here is variational data assimilation based on balanced proper orthogonal decomposition (BPOD) to identify uncertain parameters in numerical models and avoids the implementation of the adjoint with respect to model input parameters. An ensemble of model simulations (forward and backward) is used to determine the model subspace while considering both inputs and outputs of the system. By projecting the original model onto this subspace an approximate linear reduced model is obtained. The adjoint of the tangent linear model is replaced by the adjoint of linear reduced model and the minimization problem is then solved in the reduced space at very low computational cost. The performance of the method are illustrated with a number of data assimilation experiments in a 2D-advection diffusion model. The results demonstrate that the BPOD based estimation approach successfully estimates the diffusion coefficient for both advection and diffusion dominated problems. The paper also proposes an efficient method for computing the observable subspace when the number of observations is large is also proposed. (C) 2018 Elsevier B.Y. All rights reserved.
机译：伴随方法已被大量用于参数估计。这需要大量的编程工作来构建伴随模型代码，并且计算成本很高，因为一个伴随模拟的成本通常会超过几个原始模型运行。此处提出的工作是基于平衡固有正交分解（BPOD）的变分数据同化，以识别数值模型中的不确定参数，并避免在模型输入参数方面实施伴随函数。在考虑系统的输入和输出的同时，使用一组模型仿真（向前和向后）确定模型子空间。通过将原始模型投影到该子空间上，可以获得近似的线性简化模型。切线模型的伴随被线性简化模型的伴随所代替，然后以极低的计算成本解决了缩小空间中的最小化问题。在二维对流扩散模型中，通过大量数据同化实验说明了该方法的性能。结果表明，基于BPOD的估计方法成功地估计了对流和扩散主导问题的扩散系数。本文还提出了一种有效的方法，用于在观测数量大时计算可观察子空间。 （C）2018年Elsevier B.Y.版权所有。

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