Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark.

中文翻译：

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基于Sinkhorn近似的贝叶斯椭圆问题的快速混合回火集成变换滤波器公式

根据部分和嘈杂的数据来识别未知参数是一项艰巨的任务，尤其是在高维和非线性设置中。对问题的高斯近似，例如集合卡尔曼反演，往往很健壮，计算量小，尽管简化了基本假设，却往往产生惊人的准确估计。然而，还有很多改进的空间，特别是关于非高斯后验分布的正确近似。回火的集成变换粒子滤波器是一种自适应顺序蒙特卡洛（SMC）方法，其中重采样基于最佳传输映射。与集合卡尔曼反演不同，它不需要关于后验分布的任何假设，因此已经证明可以为非线性非高斯逆问题提供有希望的结果。但是，提高的精度带来了更高的计算复杂性，并且该方法在高维问题中不像集合卡尔曼反演那样健壮。在这项工作中，我们将熵启发的正则化因子添加到潜在的最佳传输问题中，从而可以通过Sinkhorn迭代大大降低高计算量。此外，在每次更新样本之前，通过集成卡尔曼反演建议步骤提高了该方法的鲁棒性，这也称为混合方法。通过在具有两种不同渗透率配置的稳态单相达西流模型上进行测试，对所引入方法的有希望的性能进行了数值验证。将结果与集合卡尔曼反演的输出进行比较，并以马尔可夫链蒙特卡罗方法的结果作为基准。