Page 85 - IJAMD-1-2

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

indicates an AM state variable in the time domain
T and spatial domain S. Figure 2 provides a schematic
representation of AM states.
Dynamical dependencies in AM can be categorized
into three types: (i) dependencies between state
properties, (ii) dependencies between rate properties, and
(iii) dependencies between state and rate properties. For
instance, the volume of a melt pool depends on the volume
of an adjacent melt pool track (a dependency between state
properties); the laser’s energy per unit property depends
on the laser speed (a dependency between rate properties);
and the melt pool’s volume is influenced by the melt pool’s
flow rate (a dependency between a state property and a
Figure 1. A schematic illustration of physical entities in melt pool rate property). Together, these three types of dynamical
generation
dependencies illustrate how physical entities transfer or
manage energy flow and evolve during AM processes.
in an AM process, while a rate property quantitatively These dependencies trigger transitions between AM states,
characterizes a flow rate or a force applied to a physical represented by the transition function in Equation II:
entity during an AM process.
• A dynamical dependency refers to the relationship g∶ φ → φ t+1 (II)
t
between the state and rate physical properties that Based on Equation II, Equation III captures the
interact with each other. For example, when a laser is concatenation of AM states, representing all the successive
applied and moves, the size of a melt pool changes. In AM state changes from the initial state of a build in the first
this AM process, the melt pool size is a state property layer (φ ) to the final state in the last layer (φ ):
influenced by rate properties like the speed of the melt 0 M M
≤
pool or the laser energy per unit length, in addition to Φ = ∏ t =0 ϕ , 0 M <∞ (III)
t
the state properties of other physical entities involved
in the process, such as the areas or temperatures of where Φ = φ ∙φ ∙⋯∙φ such that φ = g (φ ) = g(g(φ )).
t–1
t
0
M
1
t–2
adjacent metal powders melting and solidifying. 4.2. AMTransformer
• At any given moment, an AM process exists in a
specific physical state, which we define as an AM state. The AMTransformer is designed to observe the physical
The magnitude of state and rate properties, such as the characteristics of AM states and their transitions over time,
shape, size, and location of the melt pool, as well as capturing the dynamic dependencies between them. In
laser energy per unit and speed, determines the AM addition, based on this understanding, the AMTransformer
states. These state and rate properties, along with their is capable of predicting future AM states. This capability is
dynamical dependencies, influence the magnitude of achieved through two fundamental components: (i) an AM
AM state changes, state transitions, and the dynamic state embedder and (ii) a transformer. Figure 3 presents
behaviors of AM processes over time. the overall architecture of the AMTransformer.
Laser AM involves various processes characterized by 4.2.1. AM state embedder
consecutive physical phenomena that occur in a layer-by- The primary objectives of the AM state embedder are
layer manner. Particularly, when the laser interacts with to (i) learn the dynamical dependencies within an
the material, dynamic changes in AM states occur as the AM state and during its state transition to the next
laser moves along its designated scanning path, and the state and (ii) encapsulate this understanding into data
material undergoes continuous melting and solidifying. To representations by projecting these dependencies and state
analyze these phenomena, we discretize the changes in AM transitions into latent-space embedding vectors.
states into T-time steps. We define AM states as a function
of a set of state properties and rate properties. An AM state The AM state embedder is an autoencoder designed
can be expressed as Equation I: for non-linear AM processes. It is an embedding network
consisting of three main elements: an encoder, a Koopman
φ = f (x , c ), φ ∈S ⊂ ℝ , t∈T ⊂ ℝ + (I) operator, and a decoder. The encoder component of the
m
t
t
t
t
where x ∈X = {x , x ,⋯, x , x } represents state properties, AM state embedder, which consists of multi-layer neural
n
1
2
n–1
t
c ∈C = {c , c ,⋯, c , c } represents rate properties, and networks, plays a crucial role in projecting the observation
1
2
n
t
n–1
Volume 1 Issue 2 (2024) 79 doi: 10.36922/ijamd.3919