SmartScan: An Intelligent Online Scan Sequence Optimization Approach for Uniform Thermal Distribution, Reduced Residual Stresses and Deformations in PBF Additive Manufacturing

Parts produced by laser or electron-beam powder bed fusion (PBF) additive manufacturing are prone to residual stresses, deformations, and other defects linked to non-uniform temperature distribution during the manufacturing process. Several researchers have highlighted the important role scan sequence plays in achieving uniform temperature distribution in PBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. To address these weaknesses, we have articulated a vision for an intelligent online scan sequence optimization approach to achieve uniform temperature distribution, hence reduced residual stresses and deformations, in PBF using physics-based and data-driven thermal models. This paper proposes SmartScan, our first attempt towards achieving our vision using a simplified physics-based thermal model. The conduction and convection 1 Corresponding author. E-mail address: okwudire@umich.edu Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 11 October 2021 doi:10.20944/preprints202110.0158.v1 © 2021 by the author(s). Distributed under a Creative Commons CC BY license. 2 dynamics of a single layer of the PBF process are modeled using the finite difference method and radial basis functions. Using the model, the next best feature (e.g., stripe or island) that minimizes a thermal uniformity metric is found using control theory. Simulations and experiments involving laser marking of a stainless steel plate are used to demonstrate the effectiveness of SmartScan in comparison to existing heuristic scan sequences for stripe and island scan patterns. In experiments, SmartScan yields up to 43% improvement in average thermal uniformity and 47% reduction in deformations (i.e., warpage) compared to existing heuristic approaches. It is also shown to be robust, and computationally efficient enough for online implementation.


INTRODUCTION
Powder bed fusion (PBF) is an increasingly popular approach for additive manufacturing (AM) of metals (and other materials). It is used in various industries, ranging from aerospace, to automotive, to biomedical. It builds 3D parts by using a high-power source of thermal energy, typically a laser or an electron beam, to selectively fuse or melt powder layer by layer. Compared with other AM techniques for metals, PBF is popular for fabricating parts with intricate features and dense microstructure at relatively high tolerances and build rates [1,2]. However, parts produced by PBF are prone to residual stresses, deformations, and other defects linked to nonhomogeneous temperature distribution during the process [1][2][3][4][5]. In order to mitigate these defects, post-process heat treatment is often required, which takes several hours or even days and increases the overall manufacturing costs [6]. Moreover, post-process heat treatment cannot rectify deformations or cracking caused by residual stresses prior to being relieved. For this reason, it is 3 preferable to avoid residual stresses and related defects as much as possible during the build process, by minimizing temperature gradients.
Several works have revealed the importance of scanning strategy in achieving uniform temperature distribution in PBF [3,4,[6][7][8][9]. The term scanning strategy is often used in the literature to refer to disparate aspects of scanning in PBF. Here, we use the term in its broadest sense which includes all process parameters associated with scanning in PBF, e.g., laser or electron beam power, scan speed, hatch spacing, scan pattern and scan sequence. Scanning strategy is often selected by round-robin testing, trial and error, or heuristics [1,3]. However, given its importance in determining temperature distribution, a growing body of research is focused on controlling various elements of scanning strategy. Review articles [1,3,10] have presented comprehensive surveys on process monitoring and control in PBF. They have identified that beam power and scan speed are the elements of scanning strategy often controlled online or offline, e.g., [11][12][13][14][15][16][17]. However, Mani et al. [1] noted that there are opportunities for different control loops beyond beam power and speed.
One such opportunity that is of particular interest to the proposed work is scan sequence.
Scan sequence refers to the order in which a pre-specified geometric scan pattern is traced. For example, two of the most commonly used scan patterns in practice are the stripe and island (see Given the importance of scan sequence, researchers have proposed new approaches to determine scan sequence offline using heuristics. For example, in the context of the island scan pattern, Kruth et al. [21] presented the least heat influence (LHI) sequence which places the next island to be scanned as far as possible from the previously scanned islands. Malekipour et al.
proposed a Genetic Algorithm Maximum Path (GAMP) sequence [22] which claimed to maximize the path connecting the centers of all islands using a genetic algorithm, even though no details of the algorithm were presented. Ramos et al. [20] proposed the intermittent strategy which avoids scanning adjacent islands consecutively by using a geometry-based formula having weights and radial thresholds. However, no systematic procedure was provided for selecting the weights and thresholds in the formula, hence making it difficult to generalize. Taken together, a major weakness of existing heuristic scan sequences is that they only rely on geometric relationships that do not accurately represent the physics of temperature distribution, and they are non-generalizable.
For example, it is not necessarily true that scanning islands that are furthest away from the prior scanned islands minimizes thermal gradients. It highly depends on the heat diffusion process, which involves much more than geometry. Reiff et al. [23] presented a concept, without details, where the hotter islands from a measured or simulated temperature map of a prior layer were scanned later than the cooler islands to prevent layer-to-layer heat accumulation. However, this islands stripes 5 approach of selecting scan sequences is not necessarily optimal as it does not consider the transient nature of thermal distribution during scanning of the current layer.
Our research envisions an intelligent approach, dubbed SmartScan, that uses physics-based models, combined with data-driven models obtained from online thermal measurements, to efficiently determine optimal scan sequence online that minimize thermal gradients layer-by-layer [24] (see Fig. 2). Three key characteristics of SmartScan are that it is model-based, optimizationdriven, and computationally efficient enough to be run online within the interlayer time of PBF processes, which is typically less than one minute. The vision of SmartScan will be achieved in phases, with increasing complexity of the models and optimization techniques adopted. Fig. 2. Flowchart of SmartScan vision for intelligent online scan sequence optimization [24].
As its original contribution, this paper (and its preliminary version [25] up to 43% and 47% improvement in average thermal uniformity and deformations, respectively, compared to existing heuristic approaches. It is also shown to be robust and computationally efficient enough for online implementation. The rest of this paper is organized as follows: Section 2 presents the simplified thermal model used for SmartScan and the approach for determining optimal scan sequences using control theory. Section 3 presents simulation case studies, while Section 4 presents experiments performed on an open-architecture laser powder bed fusion (LPBF) machine to demonstrate the effectiveness of the proposed SmartScan approach. Section 5 concludes the paper and discusses our future work.

PROPOSED SMARTSCAN APPROACH
This section discusses the simplified thermal modeling of the PBF process using the FDM [13], reduction of the higher-order FDM model using radial basis functions [26], and an optimization approach based on control theory to find the best scan sequence for a layer.

Simplified Finite Difference Thermal Model and State Space Representation
In the simplified model presented in this section, a single layer of PBF is assumed. Only conductive and convective heat transfer are assumed to occur within the layer, and/or between the layer and its surroundings. Radiative heat transfer, latent heat effects, Marangoni convection, and other melt pool phenomena, are ignored. The simplified model is representative of the re-scanning process in PBF [27], or the plate marking process often used to evaluate the effects of heat accumulation and scanning strategies in PBF, e.g., [5,28]. Without loss of generality, LPBF is assumed in the rest of this paper.
where T is the temperature, x, y and z are the spatial coordinates, t is time and u is the power per unit volume. The FDM can be used to discretize Eq. (1) to obtain where Δx, Δy and Δz are the dimensions of each element (see Fig. 3), i, j and k are the spatial indices of the elements, l is the temporal index (i.e., t = lΔt), Δt is the time step and T(i,j,k,l) is the temperature of the element located at (i,j,k) at time l. Rearranging Eq.
(2) gives the state equation where Q, λ, P, Rb and rb are the heat flux, absorptance, laser power, laser beam spot radius and distance to the beam center, respectively. Eq. (4) is integrated over the beam area and the equivalent heat is applied uniformly over the area of the heated element.
The FDM is an excellent method for developing our simplified model for SmartScan because it is versatile. It can accommodate arbitrary layer geometries and allow for a variety of boundary conditions, e.g., convection, isothermal or adiabatic. For example, convection at the top surface can be incorporated into the model using the heat sink solution [29] as shown in Fig. 3.
The power per unit volume term in Eq.
(2) for the top-surface elements can be expressed as where us and uconv respectively denote the contributions of the laser source and convection to the total power for the element. The convection term can be expressed as where h and Ta denote the convection coefficient and ambient temperature, respectively. The where np is the number of time steps required to trace a feature (e.g., stripe or island) of the pattern.
Note that the state equation given by Eq. (9) has a sampling time npΔt.
Remark 1: Notice that the point-to-point positioning time of the laser is not included in the formulation above because it is negligible compared to the time spent scanning, as observed by Mugwagwa et al. [5]. This is because the point-to-point positioning speed (also known as jump speed) is typically 5 to 10 times higher than the scanning speed. Also, it is assumed in Eq. (9) that the number of time steps needed to scan each feature is constant. This is often the case with stripe and island patterns of fixed dimension.

Model Reduction using Radial Basis Functions
Computation and optimization using the FDM model can become cumbersome as the number of elements/states grow (for example, due to an increase in the size of the layer or the addition of a substrate to the model). This section describes the use of radial basis functions to reduce the higher-order FDM model. Radial basis functions have been used for thermal modeling of PBF in the literature, e.g., [30].
For any given time step, l, the temperature T at location (i,j,k) can be expressed using radial   (10) where ε is the shape parameter; φ is the radial basis function, [ip jp kp] T is the location of the representation elements; s is the number of representation elements; and rp (p = 1, 2, …, s) is the Euclidean distance between the element at (i, j, k) and the representation element (ip, jp, kp). In the matrix form, Eq. (10) can be expressed as If we consider the temperature of all elements in a layer, the state vector T (from Eq. (9)) can be expressed as where W = [w1 w2 … ws] T and Mt is obtained by aggregating m for all elements in the model. The where rpq is the Euclidean distance between elements (ip, jp, kp) and (iq, jq, kq). The solution to the 12 linear equation is given by Substituting Eq. (14) into Eq. (12) gives Substituting Eq. (15) into Eq. (9) gives I is the identity matrix. Hence, the transformed (reduced) state-space equation using radial basis functions is given by Remark 2: Equation (18) has reduced the FDM model from the total number of ne elements in the original formulation in Eq. (9) to the s number of representation elements, where s << ne. This will enable more efficient computation and optimization for larger models.

Scan Sequence Optimization using Control Theory
Based on the assumption that each layer in LPBF can be divided into similar features, such as stripes or islands, for the purpose of scanning (see Fig. 1), the objective is to find an optimal scan sequence such that at the end of scanning each feature the following temperature uniformity 13 metric R(lp) is minimized (19) where  (20) where I is the identity matrix, 1 is a row vector whose elements are all equal to 1, and 0 is a null matrix used to account for any elements of Tr(lp) that are not needed to calculate R(lp)e.g., Ta.
The optimization problem can be formulated as The objective of the optimization problem can be written as eq r p eq eq r p eq eq eq p eq p eq eq eq eq eq p r p eq eq eq eq eq p r p eq eq eq eq r p l ll ll ll ll The last term of the summation in Eq. (22) is independent of ueq(lp), thus it does not affect the optimization. The vector ueq(lp) has one element equal to 1 and all others equal to 0 which results in only the diagonal terms of TT eq eq eq eq B C C B affecting the summation. Hence, the optimization problem can be reformulated as eq eq eq eq eq eq eq eq r p diag l where λi are the elements of λ. Since Γ and Λ are known a priori, they can be pre-computed offline.
Accordingly, the process for determining optimal scan sequence using the proposed SmartScan is summarized in Fig. 5.

Comparative Evaluation of Thermal Uniformity
Here, we demonstrate the effectiveness of the proposed SmartScan approach in terms of optimizing thermal distribution using two case studies: (1) an island scan pattern (see Fig. 1(a)); and (2) a stripe scan pattern (see Fig. 1(b)). In both cases, we assume that an area of 5 cm   [33] 22.5 Diffusivity, α (m 2 /s) [33] 5.632 × 10 −6 Melting temperature, Tm (K) [33] 1658 Convection coefficient, h (W/(m 2 K)) [31] 25 Initial temperature, T(x,y,z,0) (K) 293 Ambient temperature, Ta (K) 293 Table 1: Parameters used in simulations (and experiments). For this case study, the 5 cm × 5 cm area to be scanned is divided into 100 (0.5 cm × 0.5 cm) islands numbered from 1 to 100 as shown in Fig. 6(a). As is typical [5,21], the direction of the scan vectors within each island is rotated by 90 o for the even numbered islands relative to the odd numbered islands (see Fig. 1(a)). Three common heuristic sequences, namely: Successive (i.e., 1, 2, 3, …, 100), Successive Chessboard (i.e., 1, 3, 5, …, 99, 2, 4, 6, …, 100), and LHI, are used as benchmarks to evaluate the proposed SmartScan approach. The LHI approach used in our numerical study is based on the tessellation algorithm proposed by Malekipour [19] because it provided an unambiguous description of its working principle and input variables, thus making it straightforward to be reproduced. The tessellation algorithm maximizes the pairwise Euclidean distance between the next island to be scanned and each of the already scanned islands (as shown in the color map of Fig. 6(b)). The first ten entries of the LHI sequence are: 1, 91, 10, 100, 45, 52, 86, 5, 41 and 23; the full LHI sequence is provided in the Appendix. Note that there is a large set of solutions that meet the condition of the tessellation algorithm, but it has no mechanism to select the optimal solution from the set of possible solutions. As a result, several islands were scanned in close proximity to one another towards the end of the scanning process (see Fig. 6(b)). Figure 6  SmartScan yields 2.19, 1.43 and 1.47 times (or 54.2%, 30.1% and 31.9%) lower mean R than the Successive, Successive Chessboard and LHI approaches, respectively. This indicates that the proposed SmartScan sequence yields better thermal uniformity compared to the competing approaches. This fact is confirmed by Fig. 8 which shows the thermal distribution of the four approaches at four instancesafter 25, 50, 75 and 100 islands are scanned. SmartScan generally 18 shows better temperature distribution than the heuristic approaches at all instances except at the beginning and at the end of the scanning process where all methods show very similar uniformity.  sequence is depicted using a color map in Fig. 9, and is listed in the Appendix. Notice that, as with the island case, the stripe SmartScan sequence is difficultif not impossibleto decipher via intuition or heuristics because it is model-based and optimization-driven. It is compared with common heuristic stripe sequences, namely, the Sequential (1, 2, 3, …, 250), Alternating (1, 3, …, 249, 2, 4, …, 250) and Out-to-in (1, 250, 2, 249, …125,126) approaches. Figure 10 shows the temperature uniformity metric as a function of number of stripes scanned. The mean value of R is reported in Fig. 10. The proposed optimal approach yields 2.59, 1.76 and 1.67 times (or 61.4%, 43.2% and 40.0%) lower mean R value than the Sequential, Alternating and Out-to-in approaches, respectively. This fact is confirmed by Fig. 11 which shows the thermal distribution of the four approaches at four instancesafter 62, 124, 186 and 250 stripes are scanned. SmartScan generally shows better temperature distribution than the heuristic approaches at all instances. sequence. The proposed SmartScan shows more uniform temperature distribution than the competing heuristic approaches. Fig. 11. Simulated temperature distribution of 6 cm × 6 cm AISI 316L stainless steel plate for stripe scan pattern at four instances during the scanning process. The proposed SmartScan shows more uniform temperature distribution than the competing heuristic approaches. 21

Evaluation of Computational Efficiency and Robustness of SmartScan
Firstly, in this section we seek to elucidate the tradeoff between temperature uniformity and computational efficiency as the number of radial basis functions used in the proposed SmartScan approach are varied.  for the online computation of the optimal scan sequences following the process outlined in Fig. 5, after the constant matrices (e.g., Γ and Λ) have been pre-computed offline. This implies that the proposed SmartScan approach is computationally efficient enough to be computed within the interlayer time of PBF. 22 Secondly, in this section, we seek to explore the robustness of SmartScan with respect to simulation parameters like conductivity, convection coefficient and absorptivity, which were obtained from generic references, hence are subject to uncertainty. Note that since diffusivity is proportional to conductivity, its uncertainty considered along with that of conductivity. Table 3 shows the mean R values for different percentage errors in conductivity, convection coefficient and absorptivity for both the island and stripe cases.  Table 3: Mean R values as functions of errors in conductivity, convection coefficient and absorptivity for island and stripe cases.

Experimental Setup and Procedure
To shown in Fig. 12 (a). The machine is equipped with a 500 W IPG Photonics 1070 nm fiber laser combined with a SCANLAB hurrySCAN galvo scanner with an F-theta lens on its z-stage. It is controlled using the Open Machine Control software that allows custom scan patterns and scan 23 sequences to be programmed by a user using macros. The PANDA 11 was retrofitted with an Optris PI 640 G7 IR camera with 33° x 25° lens/ f =18.7mm, capable of capturing thermal images over temperature ranges from −20 o C to 1500 o C at frame rates of up to 125 Hz. The experiments involved marking a 5 cm × 5 cm area on AISI 316L stainless steel (SS) plates of dimensions L × W × H = 6 cm × 6 cm × 1 mm. As shown in Fig. 12 (b), each SS plate was placed in the 6.2 cm × 6.2 cm interior of a 3D printed frame attached to the PANDA 11 machine's 27.9 cm × 27.9 cm build plate, where the plate rested on four thermal-insulating washers (Misumi Part # DJW10-3-3 with thermal conductivity of 0.24 W/(mK)). The washers minimized conductive heat transfer between the SS plate and the build plate. This allowed the experimental setup to better match the simulation setup of Sec. 3, which did not include heat transfer to the build plate. The SS plates were not constrained in any way during the experiments, allowing them to deform freely under the thermal stresses induced by the laser marking process.
The process parameters used to mark each plate are listed in Table 1, which are the exact same 24 parameters as used in the simulations. An additional parameter not included in Table 1 is the laser jump speed which was 6000 mm/s.
Each plate was scanned twice using the sequence being evaluated to amplify the thermal deformations induced in the plate. After the first scan was performed, the plate was allowed to cool to the ambient temperature before it was re-scanned. Using the IR camera, the apparent temperature of the plates was recorded at 4 frames per second during each experiment and the results exported as CSV files for processing in MATLAB. The recorded temperatures are apparent because the emissivity of the SS plate was not experimentally calibrated. It was selected as 0.35, based on typical values for stainless steel. However, actual emissivity is highly dependent on a variety of factors hence it must be calibrated carefully to obtain accurate absolute temperatures.
However, for the purposes of this paper, apparent temperatures are sufficient. This is because it is the relative, not the absolute, values of the temperatures that are important for evaluating temperature distribution.
To measure their deformations, the marked plates were each laser scanned using a Romer Absolute Arm (Hexagon AB, Sweden) model # 7525SI with a scanning accuracy of 63 μm. The plates were placed on a flat table upside down and their bottom surfaces scanned to determine their deformed shapes. The resulting point clouds were exported to MATLAB for processing.

Case 1: Island Scan Pattern
The same island scan sequences discussed in Sec. 3 were evaluated in experiments. Figure   13 shows  Experimentally measured temperature distribution of 6 cm × 6 cm AISI 316L stainless steel plate for the island scan pattern at four instances during the scanning process. The proposed SmartScan shows more uniform temperature distribution than the competing heuristic approaches Figure 15 shows a picture of the scanned plates while Fig. 16 shows the deformation profiles of each of the plates. The maximum deformations of the plate marked using SmartScan is 1.8, 1.75 and 1.7 times (or 45%, 43% and 41%) lower than those of the plates marked using Successive, Successive Chessboard and LHI, respectively. Similarly, the mean deformations of the plate marked using SmartScan is 1.56, 1.55 and 1.53 times (or 36%, 35% and 35%) lower than those of the plates marked using Successive, Successive Chessboard and LHI, respectively. These clearly demonstrates that the proposed SmartScan generates significantly lower internal thermal stresses than the competing approaches. 27 The scanning (cycle) time for executing each sequence on the PANDA 11 machine is listed in Table 4. The proposed SmartScan took 2.7% longer than both the Successive and Successive Chessboard, and 1.9% longer than LHI, due to the fact that it required the laser to jump around more than the competing methods. This shows that the performance improvement of SmartScan did not come at the expense of significantly increased scanning time compared to the heuristic approaches. Fig. 15. Picture of 6 cm × 6 cm AISI 316L stainless steel plates after laser marking using the four island scan sequences under study. Observe that the plate marked using the proposed SmartScan scan sequence shows much less deformation than those marked using the competing heuristic approaches Fig. 16. Measured deformation profiles of 6 cm × 6 cm AISI 316L stainless steel plates using the four island scan sequences under study. The numbers in parentheses are respectively the maximum and mean deformations of each plate in mm. Notice that the proposed SmartScan shows significantly lower deformations than the competing heuristic approaches. The plates were each scanned upside down.

Case 2: Stripe Scan Pattern
The stripe scan sequences discussed in Sec. 3 were evaluated in experiments. Figure 17 shows the R values of the tested sequences, calculated from the measured apparent temperatures, as a function of time. The time axis is normalized by the total number of islands scanned such that the end time corresponds to the completion of the 250 th stripe, and the intermediary time steps approximate the number of stripes scanned at each time step. Similar to the simulations, the Sequential method shows the least uniform temperature distribution while the proposed SmartScan sequence generally exhibits the most uniform temperature distribution throughout the scanning process. The mean R value for SmartScan is 1.8, 1.5 and 1.6 times (or 43%, 35% and 38%) lower than those of the Sequential, Alternating and Out-to-in approaches, respectively. This confirms the findings in the simulations that the proposed SmartScan sequence yields better thermal uniformity compared to the competing approaches. This fact is confirmed by Fig. 18 which shows the thermal distribution of the four approaches at four instancesafter 62, 124, 186 and 250 stripes were scanned. SmartScan generally shows better temperature distribution than the heuristic approaches at all instances.  Fig. 18. Experimentally measured temperature distribution of 6 cm × 6 cm AISI 316L stainless steel plate for the stripe scan pattern at four instances during the scanning process. The proposed SmartScan shows more uniform temperature distribution than the competing heuristic approaches. Figure 19 shows a picture of the scanned plates while Fig. 20 shows the deformation profiles of each of the plates. The maximum deformation of the plate marked using SmartScan is 1.4, 1.9 and 1.3 times (or 29%, 47% and 21%) lower than those of the plates marked using the Sequential, Alternating and Out-to-in approaches, respectively. Similarly, the mean deformation of the plate marked using SmartScan is 1.3, 1.8 and 1.2 times (or 21%, 46% and 16%) lower than those of the plates marked using the Sequential, Alternating and Out-to-in approaches, respectively.
These clearly demonstrates that the proposed SmartScan generates significantly lower internal thermal stresses than the competing heuristic approaches. Fig. 19. Picture of 6 cm × 6 cm AISI 316L stainless steel plates after laser marking using the four stripe scan sequences under study. Observe that the proposed SmartScan scan sequence shows less deformation than the competing heuristic approaches. Fig. 20. Measured deformation profiles of 6 cm × 6 cm AISI 316L stainless steel plates using the four stripe scan sequences under study. The numbers in parentheses are respectively the maximum and mean deformations for each plate. Notice that the proposed SmartScan shows significantly lower deformations than the competing heuristic approaches.
The scanning (cycle) time for executing each sequence on the PANDA 11 machine is listed in  Table 5: Scanning time for stripe scan sequences.

CONCLUSIONS AND FUTURE WORK
This paper has presented a new approach, called SmartScan, for optimally determining scan sequences in powder bed fusion (PBF) additive manufacturing in order to attain more uniform temperature distribution, reduced residual stresses and deformations. What makes SmartScan unique is that it is an intelligent approach that is model-based, optimization-driven and computationally-efficient enough to be executed online. It is paradigm shift away from existing approaches for determining scan sequences which depend on trial-and-error or geometry-based heuristics. Our first attempt at SmartScan, detailed in this paper, is achieved using a simplified finite difference model of PBF consisting of only heat conduction and convection. The model order is reduced using radial basis functions and the optimal sequences that minimize a thermal uniformity metric are determined efficiently using control theory.
Simulations and experiments involving laser marking of AISI 316L stainless steel plates using stripe and island scan patterns show that SmartScan drastically improves thermal uniformity and thermal-stress induced deformations compared to well-known heuristic approaches. Moreover, it is computationally efficient enough to be run online and is reasonably robust to errors in model parameters. The use of a thermal model based on the finite difference method makes SmartScan amenable to a wide range of geometries and boundary conditions encountered in PBF. Moreover, even though SmartScan was discussed in the context of stripe and island scan patterns, which are very popular in practice, it is applicable to a variety of other scan patterns with repeating features, like fractals [34] and varying-helix islands [35]. However, a key limitation is that the model used for SmartScan considers only one scanned layer and does not include the physics of the powder melting process. Hence, it is currently only applicable to the layer re-scanning process in PBF [27], or the plate marking process often used to evaluate the effects of heat accumulation and scanning 32 strategies in PBF, e.g., [5,28]. Future work will be focused on improving the SmartScan approach by incorporating more advanced models of PBF, e.g., powder melting related phenomena, using a combination of physics-based and data-driven approaches. Multiple scanned layers will also be considered. These improvements in the models used in SmartScan will likely necessitate new scan sequence optimization techniques to handle their increased complexities while maintaining high computational efficiency.

DECLARATION OF COMPETING INTEREST
The Regents of the University of Michigan have applied for patents related to SmartScan. Addit. Manuf., 31, p. 100985.