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.

翻译：多保真（MF）建模是一种强大的统计方法，能够智能融合来自不同保真度源的数据。该方法在预测激光定向能量沉积（L-DED）熔池几何形貌方面具有重要应用前景。使用多保真代理融合分层熔池模型的主要挑战在于输入空间的变异性。为解决该问题，本文提出了一种新颖的构建多保真代理方法，通过集成在异构输入空间上运行的不同复杂度模型来预测熔池几何形貌。第一个热模型包含五个输入参数，即激光功率、扫描速度、粉末流量、载气流量和喷嘴高度。相比之下，第二个热模型仅能处理激光功率和扫描速度。通过建立异构输入空间之间的映射，可将五维空间变形为伪二维空间。随后采用基于高斯过程的协同克里金法对预测结果进行融合。由此产生的异构多保真高斯过程（Het-MFGP）代理不仅提高了预测精度，还通过减少对高维、高保真热模型的评估次数提升了计算效率。研究结果凸显了将Het-MFGP应用于L-DED熔池行为建模的优势。该框架成功展示了如何利用多模态数据，并处理某些输入参数难以建模或测量的场景。