Modeling the Transient Thermal Process for the Blown Powder Directed Energy Deposition Process as a Neural Ordinary Differential Equation
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The transient heat partial differential equation can be incredibly costly to simulate with numerical methods given temperature dependent material properties, highly nonlinear physics such as radiation and evaporation, and a fine mesh resolution for accurate results. To feasibly model the problem, some complexities must be sacrificed for the sake of computational cost. Analytical models are some of the fastest methods to evaluate the problem by converting the problem to an ordinary differential equation. These analytical models, however, simplify the problem to its most basic form. This work converts the high-fidelity heat equation to a Neural Ordinary Differential Equation (NODE) to be quickly evaluated like an analytical model for all nonlinearities. This neural network is trained on a few high-quality simulations to predict the change in temperature over time for any problem. Standard ordinary differential equation solvers can then be used to evaluate the full transient time history, allowing for a choice of accuracy or speed based on these rigorously tested mathematical integrators. The results show good agreement with the simulation data calibrated against experiments with results faster than the actual process.