A Physics-Guided Neural Network Dynamical Model for Droplet-Based Additive Manufacturing

Abstract

This article develops a physics-guided data-driven model for the height evolution of parts printed in droplet-based additive manufacturing. The proposed model is a convolutional recurrent neural network (ConvRNN) whose structure is derived based on the physical understanding of mass conservation during the height evolution. Because of this physics-guided model structure, the model parameters obtained are invariant to the geometry of the printed part and thus portable from one geometry to another, the conditions on physical stability of the evolution translate directly to training stability of the neural network, and the data required to train this model are much less compared to a pure black-box model. These aspects of the model are validated experimentally on an inkjet 3-D printing setup. The proposed model outperforms a black-box off-the-shelf multilayer perceptron (neural network) by using about two orders of magnitude less data for training, at the same time delivering <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.7\times $ </tex-math></inline-formula> smaller rms error on test data. The proposed model is also compared with a state-of-the-art reduced order linear model and shows <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.4\times $ </tex-math></inline-formula> smaller rms error on test data. Finally, experimental results also underline that the model parameters learned are geometry invariant, that is, the model parameters trained on one geometry can be used to predict the height map evolution for other geometries without relearning.