Solving inverse problems, where we find the input values that result in desired values of outputs, can be challenging. The solution process is often computationally expensive and it can be difficult to interpret the solution in high-dimensional input spaces. In this paper, we use a problem from additive manufacturing to address these two issues with the intent of making it easier to solve inverse problems and exploit their results. First, focusing on Gaussian process surrogates that are used to solve inverse problems, we describe how a simple modification to the idea of tapering can substantially speed up the surrogate without losing accuracy in prediction. Second, we demonstrate that Kohonen self-organizing maps can be used to visualize and interpret the solution to the inverse problem in the high-dimensional input space. For our data set, as not all input dimensions are equally important, we show that using weighted distances results in a better organized map that makes the relationships among the inputs obvious.

翻译：求解反问题（即找出使输出达到预期值的输入变量）往往颇具挑战。求解过程通常计算成本高昂，且在高维输入空间中难以解释结果。本文以增材制造中的实际问题为例，针对上述两大难题展开研究，旨在降低反问题求解难度并提升结果利用效率。首先，针对反问题求解中常用的高斯过程代理模型，我们描述了如何通过简单改进锥化方法，在保持预测精度的前提下大幅提升代理模型的计算速度。其次，我们证明了Kohonen自组织映射可用于高维输入空间中反问题求解结果的可视化与解释。针对我们的数据集（各输入维度重要性不同），研究表明采用加权距离能够优化映射的组织结构，使输入变量之间的关联关系更为清晰。