Page 91 - IJAMD-1-2

International Journal of AI for
Materials and Design
AMTransformer for process dynamics

Following the proposed method, the case study properties in the laser AM process. These state properties of
systemically matched the state and rate property features the LPBF process are expressed as x , and the observation
L
i
at each time step to generate concatenations of consecutive data ( z L ) represents these properties. Simultaneously,
x i
AM states. Figure 9 details this process. At time step i, an rate property observation data ( z L ) represents velocity
c i
MPM image mainly focuses on the melt pool’s top surface (c i,laser_v ) and energy density (c i,laser_d ) obtained from process
area (e.g., size and morphology), which can be expressed as control data. The observed data on state and rate properties
a state property of the melt pool (x i,mp ). Melt pool location (Z) is then provided as input to the AMTransformer in
i
(x i,mp_loc ), and laser power (x i,laser_p ) also represent state sequential order.
5.3. Melt pool prediction of the AMTransformer
To handle the input data, the AM state embedder
incorporated CNNs into its architecture. In this case
study, the AM state embedder comprised four 2D
convolutional layers in an encoder and four 2D transposed
convolutional layers in a decoder. The AM state embedder
is designed to combine multiple observed inputs, each
representing an AM state ( ), to produce a single
embedding vector (ε ). This embedding vector serves as
i
a latent representation of the AM state, encapsulating the
state transition characteristics of the LPBF process. The
Koopman operator within the AM state embedder then
captures the local dynamic dependencies, as depicted in
Figure 9B. In this case study, the latent vector embedding
had 128 dimensions. We used rectified linear units as the
Figure 8. An illustration of melt pool monitoring image pre-processing,
with zoomed-in views of the original and denoised images to demonstrate activation function for the AM state embedder, leveraging
the improvement in image quality its simplicity and effectiveness in mitigating the vanishing

A C

B

Figure 9. Diagram illustrating the implementation and operation of the AMTransformer within the case study. (A) An example of the laser powder bed
fusion (LPBF) layer from the case study, showing data and target dynamical dependencies. Each dot represents a melt pool along the laser scanning path,
with the shaded area indicating the observed melt pool region used to learn the dependencies captured in functions f and g. (B) The additive manufacturing
(AM) state embedder operation and LPBF data flow: the circle represents observed data (Z), including observation of state and rate properties. The
i
rounded square denotes AM embedding, encapsulating dynamic dependencies within AM states. The Koopman operator captures linear local state
transitions. (C) The transformer operation and its LPBF data flow: the transformer processes all embeddings to reveal the adjacent melt pool region
influencing the current melt pool (red dot) from a spatiotemporal perspective. Multi-head attention and multiple decoder layers consider the relationships
among embeddings of the LPBF process, enabling the learning of non-linear and non-local dynamics. The decoder’s output, which is a contextualized
embedding, is passed through a linear layer followed by a softmax function, converting it into a probability. The highest probability event is selected as the
prediction of the future LPBF states.

Volume 1 Issue 2 (2024) 85 doi: 10.36922/ijamd.3919