Data Mining for Faster, Interpretable Solutions to Inverse Problems:A Case Study Using Additive Manufacturing

Abstract

Solving inverse problems, where we nd the input values that result in desired values of outputs, can be challenging. The solution process is often computationally expensive and it can be di cult 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 modi cation 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