We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to identify the coherent structure we wish to track; a maximum likelihood estimator to identify a Gaussian model of the coherent structure; and a nonlinear interpolation strategy that relies on optimal transportation maps between Gaussian distributions. We show that well-known self-similar solutions can be recast in the frame of optimal transportation by appropriate rescaling; we further present several numerical examples to motivate our proposal and to assess strengths and limitations; finally, we discuss an extension to deal with more complex problems.

翻译：我们提出了一个基于高斯模型最佳运输的通用(即独立于基本模型之外)内插技术,用于处理以参数对流法为主的问题。这个方法依靠一个标尺测试功能来确定我们希望跟踪的一致结构;一个最有可能确定一致结构高斯模型的估算器;以及一个非线性内插战略,依靠高斯分布之间的最佳运输图。我们表明,通过适当的调整,可以在最佳运输框架内重新制定众所周知的自我相似的解决办法;我们进一步提出几个数字例子,以激励我们的提议,评估优势和局限性;最后,我们讨论扩大范围,以应对更复杂的问题。