Data Mining for Faster, Interpretable Solutions to Inverse Problems: A Case Study Using Additive Manufacturing
This work addresses inverse problem-solving for additive manufacturing, offering incremental improvements in speed and interpretability.
The paper tackled the computational expense and interpretability challenges in solving inverse problems by proposing a modified Gaussian process surrogate for speed and using Kohonen self-organizing maps for visualization, achieving substantial speed-up without accuracy loss and better-organized maps with weighted distances.
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.