Multi-fidelity surrogate with heterogeneous input spaces for modeling
  melt pools in laser-directed energy deposition
Nandana Menon Amrita Basak
Multi-fidelity (MF) modeling is a powerful statistical approach that can
intelligently blend data from varied fidelity sources. This approach finds a
compelling application in predicting melt pool geometry for laser-directed
energy deposition (L-DED). One major challenge in using MF surrogates to merge
a hierarchy of melt pool models is the variability in input spaces. To address
this challenge, this paper introduces a novel approach for constructing an MF
surrogate for predicting melt pool geometry by integrating models of varying
complexity, that operate on heterogeneous input spaces. The first thermal model
incorporates five input parameters i.e., laser power, scan velocity, powder
flow rate, carrier gas flow rate, and nozzle height. In contrast, the second
thermal model can only handle laser power and scan velocity. A mapping is
established between the heterogeneous input spaces so that the five-dimensional
space can be morphed into a pseudo two-dimensional space. Predictions are then
blended using a Gaussian process-based co-kriging method. The resulting
heterogeneous multi-fidelity Gaussian process (Het-MFGP) surrogate not only
improves predictive accuracy but also offers computational efficiency by
reducing evaluations required from the high-dimensional, high-fidelity thermal
model. The results underscore the benefits of employing Het-MFGP for modeling
melt pool behavior in L-DED. The framework successfully demonstrates how to
leverage multimodal data and handle scenarios where certain input parameters
may be difficult to model or measure.