Page 82 - IJAMD-1-2

International Journal of AI for
Materials and Design

ORIGINAL RESEARCH ARTICLE
AMTransformer: A Koopman theory-based

transformer for learning additive manufacturing
dynamics in laser processes

Suk Ki Lee and Hyunwoong Ko*

School of Manufacturing Systems and Networks, Ira A. Fulton Schools of Engineering, Arizona State
University, Mesa, Arizona, United States of America

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
*Corresponding author:
Hyunwoong Ko dependencies across multiple scales. Our experiments, conducted using melt pool
(hyunwoong.ko@asu.edu) data from a laser powder bed fusion process, demonstrate that the AMTransformer
Citation: Lee SK, Ko H. outperforms traditional transformer and convolutional long short-term memory
AMTransformer: A Koopman models. Specifically, the AMTransformer achieved structural similarity, mean
theory-based transformer for absolute error, and accuracy metric values of 0.9206, 0.0009 mm , and 92.73%,
2
learning additive manufacturing respectively. These results indicate the AMTransformer’s superior ability to predict
dynamics in laser processes. Int J
AI Mater Design. 2024;1(2):3919. future AM states, attributed to its improved learning of complex AM dynamics. By
doi: 10.36922/ijamd.3919 combining linear Koopman-based methods with non-linear transformer-based
Received: June 12, 2024 approaches, the AMTransformer significantly improves data-driven modeling for
AM, providing a more comprehensive understanding of AM dynamics. Furthermore,
Accepted: August 9, 2024
the generalizability of the proposed method facilitates the expansion of the model’s
Published Online: September 2, 2024 scope and enhances its applicability across various fields.
Copyright: © 2024 Author(s).
This is an Open-Access article
distributed under the terms of the Keywords: Additive manufacturing; Koopman theory; Laser AM dynamics; Machine
Creative Commons Attribution learning; Predictive modeling; Transformer
License, permitting distribution,
and reproduction in any medium,
provided the original work is
properly cited.
Publisher’s Note: AccScience 1. Introduction
Publishing remains neutral with Additive manufacturing (AM) is a revolutionary technique in modern manufacturing
regard to jurisdictional claims in
published maps and institutional that enables the production of products with enhanced performance characteristics,
affiliations. often unattainable with conventional methods. Through its layer-by-layer manufacturing

Volume 1 Issue 2 (2024) 76 doi: 10.36922/ijamd.3919