Bayesian inference with coordinate transformations and polynomial chaos for a Gaussian process with a parametrized prior covariance model was introduced in Sraj et al. (Comput Methods Appl Mech Eng 298:205–228, 2016a) to enable and infer uncertainties in a parameterized prior field. The feasibility of the method was successfully demonstrated on a simple transient diffusion equation. In this work, we adopt a similar approach to infer a spatially varying Manning’s n field in a coastal ocean model. The idea is to view the prior on the Manning’s n field as a stochastic Gaussian field, expressed through a covariance function with uncertain hyper-parameters. A generalized Karhunen-Loève (KL) expansion, which incorporates the construction of a reference basis of spatial modes and a coordinate transformation, is then applied to the prior field. To improve the computational efficiency of the method proposed in Sraj et al. (Comput Methods Appl Mech Eng 298:205–228, 2016a), we propose to use two polynomial chaos expansions to (i) approximate the coordinate transformation and (ii) build a cheap surrogate of the large-scale advanced circulation (ADCIRC) numerical model. These two surrogates are used to accelerate the Bayesian inference process using a Markov chain Monte Carlo algorithm. Water elevation data are inverted within an observing system simulation experiment framework, based on a realistic ADCIRC model, to infer the KL coordinates and hyper-parameters of a reference 2D Manning’s field. Our results demonstrate the efficiency of the proposed approach and suggest that including the hyper-parameter uncertainties greatly enhances the inferred Manning’s n field, compared with using a covariance with fixed hyper-parameters.

中文翻译：

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使用广义Karhunen-Loève展开和多项式混沌的理想化沿海海洋模型中空间变化的Manning n系数的贝叶斯推断

在Sraj等人中引入了具有参数化先验协方差模型的高斯过程的坐标变换和多项式混沌的贝叶斯推断。（Comput Methods Appl Mech Eng 298：205–228，2016a）以启用和推断参数化先验字段中的不确定性。在一个简单的瞬态扩散方程上成功证明了该方法的可行性。在这项工作中，我们采用类似的方法来推断沿海海洋模型中空间变化的曼宁n场。我们的想法是要查看有关曼宁先前ñ场作为随机高斯场，通过具有不确定超参数的协方差函数表示。然后将广义的Karhunen-Loève（KL）扩展合并到空间域中，该扩展合并了空间模式的参考基础和坐标转换的构造。为了提高Sraj等人提出的方法的计算效率。（Comput Methods Appl Mech Eng 298：205–228，2016a），我们建议使用两个多项式混沌展开来（i）逼近坐标变换，并且（ii）建立廉价的大规模先进循环（ADCIRC）数值替代模型。这两个代理用于使用马尔可夫链蒙特卡洛算法来加速贝叶斯推理过程。在观测系统模拟实验框架内将水位高程数据反转，基于现实的ADCIRC模型，以推断参考2D Manning场的KL坐标和超参数。我们的结果证明了所提方法的有效性，并建议包括超参数不确定性会大大增强推断的曼宁定律。n字段，与使用具有固定超参数的协方差相比。