Machine learning‐enabled optimization of melt electro‐writing three‐dimensional printing

Melt electrowriting (MEW) is a solvent‐free (i.e., no volatile chemicals), a high‐resolution three‐dimensional (3D) printing method that enables the fabrication of semi‐flexible structures with rigid polymers. Despite its advantages, the MEW process is sensitive to changes in printing parameters (e.g., voltage, printing pressure, and temperature), which can cause fluid column breakage, jet lag, and/or fiber pulsing, ultimately deteriorating the resolution and printing quality. In spite of the commonly used error‐and‐trial method to determine the most suitable parameters, here, we present a machine learning (ML)‐enabled image analysis‐based method for determining the optimum MEW printing parameters through an easy‐to‐use graphical user interface (GUI). We trained five different ML algorithms using 168 MEW 3D print samples, among which the Gaussian process regression ML model yielded 93% accuracy of the variability in the dependent variable, 0.12329 on root mean square error for the validation set and 0.015201 mean square error in predicting line thickness. Integration of ML with a control feedback loop and MEW can reduce the error‐and‐trial steps prior to the 3D printing process, decreasing the printing time (i.e., increasing the overall throughput of MEW) and material waste (i.e., improving the cost‐effectiveness of MEW). Moreover, embedding a trained ML model with the feedback control system in a GUI facilitates a more straightforward use of ML‐based optimization techniques in the industrial section (i.e., for users with no ML skills).

tions.The MES, specifically in tissue engineering, is widely preferred due to its non-woven fiber diameters for the application of scaffolds where high porosity is desired. [5,10]On the other hand, the MEW defines well-ordered fiber structures and patterns to achieve strong, durable, and organized high porosity scaffold [8] with small fiber diameters. [8,11]EW's precision has been embedded in the fabrication of microchannel systems [8,12] and microfluidics [11] overcoming the conventional techniques. [12]Its application extends across many sectors from optics to photonics and lap-on-chip devices. [8,11]The accuracy of having such high craft precision for microscale application is due to its control over the jetting process and stability. [13]Many parameters influence this stability such as applied pressure, electric field, and collector speed, understanding their interdependence and relation is an area of interest. [13] MEW device consists of a printing head with a heating system that melts the material stored in a syringe and delivers it to a metal nozzle.A computer-aided translation system is installed in the MEW head, allowing for direct writing onto a collector.The extrusion of the material melting through the nozzle is forced by a delivery system (typically air pressure), and an applied potential difference between the nozzle and the collector generates an electrical field.When an electric field is applied to a fluid drop, it concentrates charges at the closest point to the collector, overcoming surface tension forces and ejecting a conicalshaped jet toward the collector.The beginning of this jet and the remaining fluid at the tip of the nozzle is termed the Taylor cone which will be generated within seconds, as soon as the applied electrical field overcomes the surface tension of the droplet at the tip of the nozzle. [14]As the Taylor cone is filled with more molten polymer, the weight of the melt begins to neeck from the initial droplet, forming a thin column.This proceeds until the forces (gravitational and charges) draw the solidified polymer to be in contact with the collector.The resulting fiber diameter can be controlled, adjusted, and directly written in varying configurations depending on the printing parameters. [15]Smalldiameter fiber placement enables the printing of porous structures known as scaffolds, which are used in the biomedical sciences. [16]To date, melt-electrowritten scaffolds have been investigated in the skin, heart valves, and musculoskeletal soft tissues, where poly-ε-caprolactone (PCL) is commonly used. [17]PCL, a Food and Drug Administrationapproved bioresorbable polymer, is the biomaterial of choice for constructing tissue-engineered melt electrowritten scaffolds due to its easy processability, low cost, and lack of immunogenicity. [18]Alternatively, when MEW is performed at collector speeds lower than the electrified jet speed, the jet buckles, similar to a column of honey falling onto toast. [19]uch mechanical buckling of a viscoelastic column produces an array of different patterns that can be modeled and predicted. [20]n this work, we introduce an innovative methodology for combining the fields of MEW, image processing, ML, and control theory to be embedded within a friendly GUI.First, samples from the MEW at different setup of printing parameters has been printed and collected.Four input parameters were used for this purpose; the pressure at which air is compressed into the MEW's nozzle, the speed at which the feed rate of material is extruded, the gap between the nozzle and printing surface, and the high voltage difference between applied between the nozzle and print bed.Second, a customdesigned algorithm image processing technique was carried out for line thickness calculation.Upon the collection of data, some prints are classified as "bad prints" as these patterns are not preferred in the real printing process.Only "good prints" were undertaken in the image processing part.Third, the dataset collected was preprocessed and trained in ML regression models where a Bayesian hyperparameter optimization has been handled.Fourth, Proportional, Integral, Derivative (PID) controllers for each of the four inputs are tuned according to the sensitivity returns of the plant (regression) model.A saturation and anti-windup configuration within the controllers were used.Finally, a GUI has been developed that provides a user-friendly interface to grant instant feedback and enhance the user experience and visual representation.

Device
We used a 3D printer (Axolotl Biosystems) with multihead components which offers versatile usage, enabling users to switch between different printing materials, methods, or applications via swapping the printheads upon the desired request of the user.The specific printer from Axolotl is equipped with an ultraviolet curing tool head that facilitates the photocrosslinking of biomaterials and bioinks, high/lowtemperature printheads that demand a high/low-temperature extrusion of several polymer types for working with bioresorbable and biocompatible materials, and a MEW printhead.
The MEW printhead can simultaneously deposit multiple layers allowing for intricate design and the integration of functionalities within a single print session.It is also capable of writing melted material with high voltage, hence the name "Melt ElectroWriting".The Axo MEW can achieve a micro-level of precision that provides a 3D fabrication of fiber scaffolds which aids in various medical applications such as tissue engineering and regenerative medicine.The printer was specifically set to electrowrite line thickness for voltages that fall in ranges of 2-3 kV, gaps of 0.2-1 mm, pressures of 1-23 psi, printhead's feedrate of 300-2000 mm/min, and a stable printhead temperature of 150 • C.

Material
The printing material used in this study was PCL.PCL is a dielectric material, which means it is an insulator that can become polarized when subjected to an electric field. [21]hen an electric field is applied to PCL, the positive and negative charges within the polymer molecules may shift and align themselves with the field direction.This phenomenon is known as polarization.Therefore, PCL is a suitable material for the MEW 3D printer that uses electric field difference (EFD) between the nozzle and the print surface to ensure a steady flow of the material out of the nozzle by overcoming the surface tension of the molten polymer, causing it to elongate and form a continuous filament or jet. [6]

Line thickness experiments
The line thickness of printed designs is of foremost importance as it can determine the print resolution and mechanical properties.In microfluidic applications, in which MEW is used for the fabrication of negative mold, [22] line thickness control is necessary to obtain the designed channel width/thickness.Decisive parameters affecting the line thickness can be cartridge temperature, print pressure, EFD between the nozzle and the printing surface, printing gap, and print speed (i.e., feed rate).The study aims to develop an ML-enabled platform through which a user can find the best combination of printing parameters (e.g., print pressure and voltage) to acquire desired line thickness without a need Images of the 3D-printed lines were taken under a microscope.A custom-designed algorithm classified straightly printed lines (labeled as "Good Prints") from curvy print outcomes (labeled as "Bad Prints" as these patterns are not preferred in the real printing process).Images with "Good" labels were binarized for better visualization and image processing (i.e., changing pixels to black and white).Next, a standard stencil card was used, on which a standard line with a predetermined thickness of 0.1 mm was drawn.The same microscope and imaging distance were used to capture the image of the standard line.Later, the image of the standard line was used to determine the thickness of the rest of the lines in the captured images.Subsequently, line thickness was collected in a CSV file which was used for machine learning (ML) algorithm training.Next, the trained ML regression model is implemented in a feedback loop using Proportional, Integral, Derivative (PID) controllers where each controller is tuned according to the sensitivity of the model.Finally, the model system can assist MEW users in determining optimum printing parameters to achieve a desired line thickness without the need for error-and-trail steps.
for error-and-trial steps, resulting in a faster process time and less material waste (Figure 1).

Printing and imaging
Firstly, using SolidWorks software, nine similar straight lines (with the same thickness of 0.2 mm) (Figure 2E) were drawn and exported to the 3D printer as G-code.The thickness of lines was set to be the same in the CAD design to minimize the effect of design and focus/study the pure effect of print parameters on the thickness of the designed lines.Next, each line was printed using a different combination of printing parameters (Figure 2F).For example, for the first set of nice lines, to study the effects of printing pressure on the line thickness, all the abovementioned printing parameters were kept constant, while the printing pressure was changed at the beginning of each line.Upon completion of the printing process, the printed design was removed from the printer to capture images of the printed lines using a microscope.All images were taken from the same lens distance to maintain a similar aspect ratio in all images.Captured images were then labeled with the printing parameters used for the 3D printing of the line in the image and fed into a custom-designed image processing algorithm for the automatic calculation of line thickness.The same process was repeated for other printing parameters (e.g., printing with different EFD while other abovementioned parameters were kept constant).The cartridge temperature was set to 150 • C during all experiments, as per the guidelines of the Axolotl company.

Custom-designed algorithm for line thickness calculation
We developed an image processing method that can automatically calculate the thickness of the line in a captured image.In the context of image processing, our developed algorithm plays a pivotal role in automatically quantifying line thickness from captured images.Commencing with the conversion of images to grayscale, it subsequently applies Gaussian blur to mitigate noise while retaining line continuity.Employing thresholding, it transforms the image into binary format, distinguishing line pixels from the background.Significantly, our method utilizes a three-by-three filter to effectively eliminate isolated black pixels, minimizing potential outliers.By systematically evaluating each column, the algorithm counts consecutive black pixels to determine line thickness.This culminates in the computation of an average thickness value.The resulting data, including image names, printing parameters (pressure, gap, and EFD), feed rate, and line thickness, are methodically stored in a CSV file.This comprehensive approach not only facilitates the precise measurement of line thickness but also enhances the utility of this data for machine learning training and GUI development in a variety of applications.Figure 3 illustrates the process where each step of the image processing method is detailed.

Machine learning
[25][26][27][28][29][30] The algorithm should first be trained on the data in the training set in which the parameters in the algorithm will be improved during the training process, and a machine learning model will be generated.It can then predict the results with new input data using the updated machine learning parameters.Supervised learning, unsupervised learning, and reinforcement learning are the most often used machine learning algorithms. [23]n ML model was developed to correlate the printer's input parameters and line thickness retrieved previously by the custom-designed algorithm for line thickness calculation.Regression models were employed to map four printer parameters and the single output line thickness captured by the algorithm.To ensure faster convergence, enhance the accuracy of ML models, and prevent numerical instabilities, the input dataset was normalized to a consistent scale ranging from [−1 1], while the output data remained unchanged.Out of a total of 168 printed samples, the dataset was divided into training and validation sets using an 80:20 ratio, where only 34 data points were reserved for validation after model training.Different ML models such as linear, vector support machine (SVM), decision trees, Gaussian process (GP), neural network (NN) along other regressions were trained with the remaining dataset.The models were assessed based on their mean squared error (MSE), root MSE (RMSE), and R 2 scores, with the aim of minimizing potential errors during both the computation and execution phases.
To optimize the performance of the various ML models, they were subjected to a Bayesian optimizer for tuning the hyperparameter optimization.Unlike grid search or random search methods which either exhaustively explore or randomly sample the hyperparameter space, the Bayesian optimizer uses an intensive search across the hyperparameter space which constructs a probabilistic model of function that maps hyperparameters with a given validation score allowing it to thoroughly explore the hyperparameter space.It then can create an approximation of the error as a function of the hyperparameters to improve the model.The learning process was set for 30 iterations which updates the model based on observed performances, hence, Bayesian optimization can more efficiently locate optimal hyperparameter configurations.Therefore, the hyperparameters were tweaked for each ML model to ensure that our models were configured in an optimal manner.Thus, enhancing their performance on the validation set.Again, model performance was evaluated based on MSE, RMSE, and R 2 scores.
F I G U R E 3 Flowchart of our developed image processing method for automatic line thickness quantification.(A) Image processing pipeline used to measure line thickness, beginning with grayscale conversion, Gaussian blur, thresholding, contour detection, and distinguishing upper and lower contours for subsequent analysis.(B) Calibration process using a reference image with a known thickness of 0.2 mm, allowing the conversion of pixel distances to actual physical distances.(C) Line thickness calculation is visually represented for various image samples, measuring pixel distances between upper and lower rectangle edges, which are then mapped to physical distances using the pixel resolution from the reference image.(D) Physical vs prediction line thickness algorithm.Sixteen samples have been randomly selected to measure their real thickness using the microscope.Compared to the image processing prediction, the performance has been reported in root mean squared error (RMSE) and R 2 scores at 0.05 and 0.9904, respectively.

Sensitivity and feedback control
Seeking to attain the results of the line thickness from our previously obtained regression model, it serves as the core plant model in the controller feedback loop.Due to the shortage of availability in the dataset, this controller design approach solves the related issue.The proposed approach is mentioned as shown in Figure 1.Each of the four inputs was controlled and managed by four PID controllers that minimized the error coming from the feedback loop.The main drawback of this method is to be able to tune all four PID controllers, hence, 12 parameters of P, I, and D combined.Despite the tedious and complicated job, tuning those parameters was guided with the help of PIDTuner and Sensitivity Analyzer apps within MATLAB and Simulink environment.
The target system behavior in the multi-input single-output (MISO) system was determined by a reference setpoint of a desired line thickness.In a feedback loop, the actual output from the plant model is subtracted from the reference point and fed into the controllers.The controllers then attempt to settle, manage, and adjust the deviation between the plant's prediction and reference setpoint by correcting new input values relayed back into the system.The loop correction is maintained as it ensures the system continually adjusts its behavior, aligning with the reference setpoint over time.
PID stands for Proportional, Integral, Derivative which are the three types of control "actions".The Proportional term amplifies the error value by a proportional gain.Essentially, it is the response to the present error in the model.The Integral term is responsible for all summation of past error values accumulated by the model.Inherently, the integral term attempts to eliminate and drive the system to zero steadystate error by an integral gain.Finally, the Derivative term anticipates the system response based on its rate of change in error.The derivative gain controls the effect of future error, thus, slowing down the rate of change in error.Each of the input parameters exhibits its own influence on the line thickness output in the plant model.The pressure and speed have the most impact on the model compared to the voltage and gap parameters.Therefore, a tuning in PID parameters was accompanied by a sensitivity analysis to assess the behavior of each input on the system.Whether one parameter is more sensitive to changes from another or more robust, etc.Additionally, the PID controllers were saturated at limits of [−1 1] in agreement with the regression model obtained earlier.

Machine learning
Several machine learning models are trained.Yet, we only picked the one that outperformed the other models in terms of RMSE, MSE, and R 2 scores.The validated scores of the regression models fall between 0.12, 0.015, and 0.93 and 0.15, 0.024, and 0.89 for RMSE, MSE, and R 2 , respectively.The MSE is the average of the squared error difference between the predicted and actual values that measures the average magnitude of the error, while the RMSE is simply the square root of the MSE which provides interpretable readings of the error magnitudes since it is in the same unit at the output.The lower of these errors the better the model's performance.The R 2 , also known as the coefficient of determination, provides a measure of how well the observed outcomes are being replicated by the model.It ranges from 0 to 1 (1 for a perfect score).These results were recorded when a Bayesian hyperparameter optimizer was utilized.The GP regression was our best model for this work which optimized five hyperparameters namely: basis function, kernel function, kernel scale, sigma, and whether standardize is on or off.The search ranges of each hyperparameter were predefined automatically.For example, the basis function could be a constant, a zero, or a linear function; the kernel function can be nonisotropic exponential, nonisotropic rational quadratic, isotropic ration quadratic, etc.For each set of ranges, the Bayesian optimizer ran for 30 iterations looking for the best outcome using the several combinations of hyperparameters within the ranges.Additionally, the acquisition function in the Bayesian optimizer was set to expected improvement per second which takes into consideration the improvement in the objection function and time required to evaluate the function.Finally, the optimized hyperparameters were found according to the selected search criteria and the training results were provided.As previously mentioned, the GP regression surpassed the performance of all other regression algorithms.This can be attributed to its ability to accurately model intricate data in non-parametric models.Moreover, GP regression effectively filters and manages noise inherent in the dataset along with uncertainties arising during training.We observed the following results for our GP regression model: the RMSE, MSE, and R 2 were recorded at 0.12329, 0.015201, and 0.93, respectively.Figure 4A provides insight into the GP regression model obtained for perfect prediction and imposed data points in the normalized range.The hyperparameters that were calculated by the Bayesian optimizer are supported in Table 1.A RMSE of 0.12329 indicates that there is a deviation in predicted line thickness by this amount.Due to the nature of the dataset, taking the average between the minimum and maximum line thickness that are within the dataset (0.0172 and 2.2635, respectively) results in around 10.8% error.This has been also proven by the remaining 34 datapoints in the testing set yielded 0.1054 for the RMSE score.
The discrepancy in scores can be explained by the limited number of prints in our experiment as it was tedious to print all these prints.Yet, a ten percent error can be accepted in our work due to the absence of other negligible factors.

Custom-design image processing algorithm
the image processing pipeline that quantifies line thickness by converting the image to a grayscale version, eliminating color information and concentrating solely on luminance values (Figure 3A).This step simplifies the subsequent computational tasks by reducing the complexity of the image.Gaussian blur is applied to the grayscale image to diminish noise and irregularities within the image, rendering it more amenable to accurate analysis while enhancing the quality of thresholding, a pivotal step in the process.Thresholding segregates the region of interest from the background by designating specific intensity levels, resulting in a binary image where lines are distinctly separated from the background.Once images are preprocessed, contour detection is applied to identify the outlines of the lines within the binary image.The algorithm segregates upper and lower contours based on their vertical positions.This distinction is vital for subsequent calculations since bounding rectangles are drawn around the identified upper and lower contours, encapsulating the upper and lower regions divided with lines within the image.Line thickness calculation is based on the distance between the lower edge of the upper rectangle and the upper edge of the lower rectangle.This measure provides an accurate and quantitative assessment of line thickness.In order to calculate physical distance instead of pixels, the thickness

Hyperparameters name Search range Optimized hyperparameters
Basis calculation algorithm was first applied to a 0.2 mm reference image in order to obtain pixel resolution (0.00275 mm) (Figure 3B).The obtained pixel resolution is then used to map pixel distance to the actual distance (Figure 3C).The image processing performance algorithm has been evaluated according to the physical real thicknesses of the line.We have considered the physical line thickness as our gold standard in order to compare the accuracy.16 lines have been measured to compare their actual line width with the prediction image processing algorithm.Figure 3 provides results of RMSE and R 2 scores with the plotted prediction versus accuracy.

Sensitivity and feedback control
in the context of sensitivity results, the PID controllers were tuned separately, and observed their impact on the output model.The sensitivity chart shows that pressure and speed had the most influence over the model as providing typically The graphical user interface (GUI) provides an informative result when using the line thickness calculation app.The user would specify the desired line thickness into the line width field, upon the calculation of the model embedded into the GUI, the pressure, speed, gap, and voltage parameters are determined and can be used in a melt electrowriting (MEW) printer.The live data plot offers a tracking curve to know whether the value is converging to the specified entered line thickness in the calculation part, or it does not.Additionally, the evaluation time helps the end-user to know how much time has elapsed if the comparison between models is needed.
a lower Proportional gain to the parameters compared to the gap and voltage, Figure 4B.On the other hand, the gap and voltage need a high Proportional value to avoid slow response and reach the setpoint quickly.Yet, a higher Proportional gain could lead to an overshoot of the system.Thus, balancing between the Proportional gain among the input parameters is required.The sensitivity analysis also provides an insight after tuning the Proportional gain whether the inputs are oscillating around the setpoint or not reaching the desired output.The integral gain is introduced into the system to eliminate long-term steady-state error.A Derivative term was needed to speed up the system's response but could also introduce overshoots and noises to the system.Again, refining the gains based on the sensitivity chart to balance between robustness and aggressiveness in the regression model was a key step in the controller design phase.Interestingly, the sensitivity chart also provided the sign correlation between the input param-eter and its output.Pressure has a negative correlation with the line thickness which indicates an inverse relationship, for example, thinner line thickness in response to increasing pressure value.Whereas the speed has a direct effect as computed.
After successive tuning of each PID controller individually, the controllers struggle to bring the MISO system to the desired setpoint.This was due to nonlinearities within the controllers when they were saturated in [−1 1] ranges.Therefore, an anti-windup strategy through back-calculation within each controller was implemented.[33] This could cause overshoot, prolong settling times, and "stuck" behavior.The anti-windup mechanism is built in the Integral gain that acts as a break whenever the saturation limits at the output are reached.The back-calculation anti-windup takes the difference between the saturated value and the actual PID output and is fed back to the integrator to subtract it from the accumulated error in the feedback loop. [33]Moreover, the back-calculation coefficient determines how aggressively the accumulated integral error is to be adjusted when the saturation occurs. [34,35]Finally, the controller designs, incorporating the anti-windup mechanism for output saturation, were correctly tuned using an untrained dataset in alignment with the provided sensitivity analysis.Figure 4C visualizes the schematic control diagram along with associated PID gains in Table 2.

Graphical user interface
A graphical user interface (GUI) of the line thickness model has been integrated within the feedback controller discussed earlier.Our primary objective is to be able to validate and operate the line thickness model where non-experienced users can utilize it.With this easy-to-use interface, users can easily monitor on running status, to know if the model is in running mode, and patiently wait for the operation to end (evaluation finished) without the need for manual interruption.The GUI allows users to enter the desired line thickness, denying negative numbers.Upon activating the calculate button, the system initializes the Simulink model in the background where it tries to track the error arising from the feedback loop of the controllers.Then finally displaying the printer's input parameters within the interface.Additionally, the GUI cannot execute another calculation while it is on the running status as shown in Figure 5.

Validation
The validation step of our work was of high importance as the development of the final product, the GUI of line thickness.
We prepared a list of some desired line thicknesses to be fabricated by the MEW.The previous lines which were printed and collected as training datasets, were specified through CAD drawings, keeping the temperature, feed rate, voltage, and gap constant while altering the pressure values to produce the dataset.However, this time, we specified the four input parameters to the printer configuration that have been predetermined by the GUI.The expected results were to show some error deviation from the actual thickness, as provided by the ML model.Yet, after postprocessing the newly validated results, the observed line thickness from the custom algorithm layout a line thick that is on average two times wider than the desired line thickness (Table 3).This claim can be explained via the error made in the regression model and the controllers' approximation of PID values.On the other side, the MEW printer's settings have been modified from the dataset collection due to technical issues with the printing heads.We have accounted for the ratio between the desired and obtained line thickness from the algorithm by defining an error factor constant, ranging between 2.2 and 2.4, to isolate and narrow down the difference.By addressing the mismatch, we were able to recreate new line thicknesses to match our desired prediction from GUI with an acceptable difference of 5-7% error after adding the error factor.

CONCLUSION
In conclusion, this study provides insight into how an MEW printer can be implemented with ML along with feedback controllers in which it can be designed and built inside a GUI for friendly use.Around 160 prints from the MEW printer were used to train different ML algorithms and based on certain criteria, the best regression model was used to represent the plant model in our feedback loop in the controller phase design.The prints were captured through a microscope and reported their input printer's parameters where each datapoint had unique inputs during the data extraction.The image classification and image processing techniques were imposed to filter and classify "good" and "bad" prints that resulted in fabrication.Upon disregarding the "bad" prints, the classified "good" prints were filtered into a custom-designed algorithm to calculate the line thickness approximation.The collected results of line thickness along with the printer's input parameters made up the dataset that was trained in regression analysis where GP regression provided the best performance with 0.12329 RMSE, 0.015201 MSE, and 0.93 R 2 scores.Moreover, to link the desired line thickness and the printer's input parameters, the model line thickness was implemented as a plant in a feedback controller loop where it returns the original model prediction from GP regression and reduces the error between the desired line thickness and model prediction from GP regression through the PID controllers.Additionally, the controllers were tuned according to the sensitivity of the input parameters using analyzer apps within the MATLAB environment.Finally, the entire system was customized and compacted to be made possible for free to access in a GUI where the users would enter the desired line thickness as wished then at background evaluation, the model would provide the printer's input parameters.The proposed methodology not only enhances the accessibility of the system but also paves the way for broader applications, ensuring that possible further improvements and fixes in the model at expertise levels.

FINAL REMARKS AND FUTURE PERSPECTIVES
The development of the line thickness prediction marked the first step toward enhancing the framework of the MEW platform.Although the work is in its current state of the art, improvements in the crucial aspects of MEW technology can be considered.Further improvements in the ML algorithms and techniques could be more efficient to utilize and investigate.That includes reinforcement learning for enhancing the performance further on the algorithm side.Additionally, a promising direction could involve a real-time adaptive control system that continuously adjusts the MEW parameters during the printing process based on the feedback information received.This requires additional setups such as sensors, high-speed recording cameras, and other integrated devices.This can further enhance the stability and precious of the MEW which allows dynamic response under uncertainties and changing conditions within the environment of the printer.Additional information can be fed into the ML model to further increase robustness and parameter optimization.

A C K N O W L E D G M E N T S
ST acknowledges Tubitak 2232 International Fellowship for Outstanding Researchers Award (118C391), Alexander von Humboldt Research Fellowship for Experienced Researchers, Marie Skłodowska-Curie Individual Fellowship (101003361), and Royal Academy Newton-Katip Çelebi Transforming Systems Through Partnership Award (120N019) for financial support of this research.Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the TÜB İTAK.This work was partially supported by the Science Academy's Young Scientist Awards Program (BAGEP), Outstanding Young Scientists Awards (GEB İP), and Bilim Kahramanlari Dernegi the Young Scientist Award.This study was conducted using the service and infrastructure of Koç University Translational Medicine Research Center (KUTTAM).

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflict of interest.

F I G U R E 1
Schematic workflow of "line thickness" calculation and training.Designed patterns were transferred to the melt electrowriting (MEW) threedimensional (3D) printer as G-code, where different printing parameters (e.g., pressure, voltage, etc.) were used to fabricate lines with different thicknesses.

F I G U R E 2
Printer Setup; (A) the melt electrowriting (MEW) (shown on top left) along with the voltage supplier.(B) The air pressure supplier pumps air to the nozzle head of MEW.(C) The MEW printhead mounted onto the Axo BiosystemPrinter (shown on top right).(D) Additionally, the Repetier-host software is used as an interface to print the specified loaded CAD files to the MEW printer (shown on the bottom right).(E) The different combinations of air pressure and federate obtained during the experimental printing of the line thickness.(F) Similar lines (with the same thickness of 0.2 mm) were drawn in three-dimensional (3D) using SolidWorks and then exported to the printer as G-code.Each line was printed using a different combination of printing parameters.

F
I G U R E 4 (A) The machine learning (ML) regression model obtained for the hyperparametrized GPR with mean squared error (MSE) of 0.0152, R 2 of 0.93, and root MSE (RMSE) of 0.12.For a normalized perfect model, the true and predicted responses are equally identified by the straight line.The observations of the dataset are shown in black dots.(B) The sensitivity analysis of the printer's inputs obtained for pressure, speed, voltage, and gap.The pressure and speed have the most impact on the model output, where the pressure has an inverse effect.While the voltage and gap have a negligible effect on the printer's thickness.(C) The designed feedback controller loop of the whole analysis.The tuning of four Proportional, Integral, Derivative (PID) controllers is accomplished based on the sensitivity chart obtained previously.The input parameters that have most of the influence (e.g., pressure and speed) would have lower Proportional gain relative to the diminished influence (e.g., gap and voltage).Integral and Derivative gains are adjusted based on the behavior and the performance of the model.TA B L E 1 Optimized hyperparameters.