Data Mining for Faster, Interpretable Solutions to Inverse Problems: A
  Case Study Using Additive Manufacturing
Chandrika Kamath Juliette Franzman Ravi Ponmalai
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.