AMTransformer: A Koopman theory-based transformer for learning additive manufacturing dynamics in laser processes

Abstract

Recent advancements in machine learning (ML) have shown unprecedented promise in understanding and predicting additive manufacturing (AM) dynamics. However, existing ML studies on AM often lack a comprehensive approach to address the multi-scale complexities inherent in AM processes and tend to employ context-specific methods. To address these limitations, we present a foundational method for formulating AM dynamics suitable for ML modeling. We then introduce a novel approach, the AMTransformer, designed to comprehend complex spatiotemporal dynamical dependencies among physical entities and their properties within the AM process. To enhance the understanding of AM dynamics, our method adapts Koopman’s theory to generate latent embeddings of AM states and their transitions, effectively extracting hidden features related to physical properties and dynamical dependencies. In addition, by utilizing the transformer’s attention mechanism, the proposed approach enhances the learning of non-local, non-linear dynamical dependencies across multiple scales. Our experiments, conducted using melt pool data from a laser powder bed fusion process, demonstrate that the AMTransformer outperforms traditional transformer and convolutional long short-term memory models. Specifically, the AMTransformer achieved structural similarity, mean absolute error, and accuracy metric values of 0.9206, 0.0009 mm2, and 92.73%, respectively. These results indicate the AMTransformer’s superior ability to predict future AM states, attributed to its improved learning of complex AM dynamics. By combining linear Koopman-based methods with non-linear transformer-based approaches, the AMTransformer significantly improves data-driven modeling for AM, providing a more comprehensive understanding of AM dynamics. Furthermore, the generalizability of the proposed method facilitates the expansion of the model’s scope and enhances its applicability across various fields.