Time-efficient surrogate models of thermal modeling in laser powder bed fusion

Two time-efficient surrogate models are proposed to emulate the nonlinear heat equation in the context of laser powder bed fusion, the performance of which is compared in accuracy and online execution time. Fast-computed numerical solvers are critical in implementing the digital twin framework in the additive manufacturing process addressing one of its main open problems: lack of quality assurance. The first surrogate model is the reduced Gaussian process emulator. It is a data-driven model equipped with a nonlinear dimension reduction scheme and manages to predict temperature profiles almost instantly (around 0.036s on average) with an accuracy of 95% for 99.38% of tests. Another surrogate model is the sketched emulator with local projection. It projects the accurate but high-dimensional finite element method solution on a low-dimensional basis and then bypasses the majority of costly computations for the temperature-dependent matrices in the projected model by randomized sketching. It has higher accuracy (97.78% of tests with relative errors below 1%) while spending comparably more time online (around 42.23s on average). Although compared with the finite element model both surrogates promote time efficiency with some minor controlled compromise in accuracy, the reduced Gaussian process emulator enables real-time implementation while the sketched emulator with local projection offers comparably higher levels of accuracy. A series of numerical experiments are carried out, which assumes a three-layer printing process with a fixed laser beam trajectory using a small number of printing control parameters as inputs, namely the laser power, scan speed, and time coordinates. Both surrogates are also principally feasible in other thermal-driven additive manufacturing to obtain better quality assurance with techniques like uncertainty management and closed-loop control.