Blackbox optimization for approximating high-fidelity heat transfer calculations in metal additive manufacturing

Heat transfer simulations play an important role in predicting solidification conditions that determine microstructure properties of additive manufactured products. High-fidelity heat transfer models, e.g., Truchas [1], provide a numerical framework capable of resolving many desired physics (e.g., thermal radiation, elemental vaporization, gas-solid-liquid interactions, etc.), but they are often too computationally expensive to simulate the solidification conditions at the AM process-scale. Recently, Stump et al. [2] proposed a low-fidelity analytical heat conduction model capable of simulating solidification conditions on the process-scale. This model makes the problem analytically tractable by neglecting many important physics that may have an impact on the accuracy of the predicted solidification conditions. An effective way of improving the accuracy of the analytical with little computational effort is to determine an optimal set of parameters that minimize the discrepancy between the low-fidelity analytical model and a high-fidelity numerical model. In this work, a model approximation problem is formulated which can be solved by leveraging blackbox optimization methods. Multiple heat sources are used in the analytical model to improve the calibration performance in a flexible framework. Two blackbox optimization methods, i.e., Bayesian optimization and directional Gaussian smoothing methods, are employed to address the challenge that the gradient of the loss function is inaccessible during optimization. The results show that the single-beam analytical model has limitations in fitting the high-fidelity model, but the proposed multi-beam analytical model provides satisfactory approximations to the high-fidelity temperature and melt pool fields.