 in machine learning. So, beside my name, you can also see three other names on the slide, Sopetra Genus, and Sasha Strum come from the Department of Manusstructured Materials, and myself and Professor Sasha Gerovsky, whom you've already had the chance to meet, come from the Department of Knowledge Technologies. So we live in times where we see the increased electrification of society which in turn increases the energy consumption. So this imposes a new request upon us to transfer to more greener energy sources, and it is upon us as scientists and conscious human beings, above all, to respond to that request. So fusion power is one of the ways to go in that direction, and it also has some obstacles that need to be overpassed if we want to ever implement it in practice. One of the greatest challenges is to find materials that are suitable to withstand high thermal loads, and without having any significant changes in their thermal mechanical properties. So the diverter is one of the most essential parts of the fusion reactor. It is situated at the bottom of the vacuum vessel, and it's in charge of extracting the heat and the ash that is produced by the fusion. It also protects from plasma contamination and ensures that the walls around the reactor are protected from the high temperatures and nutrient bombardment. So that being said, we can conclude that there are quite some requirements for choosing the right diverter materials. It needs to have high melting points, it needs to have low activation, good mechanical properties that operate in conditions, high thermal conductivity, and high thermal shock resistance. So by now I've said thermal like 10 times, which leads us to a suggestion that we need to choose a material that has a very high melting point. And tungsten is kind of a natural choice because it's the metal with the highest melting point, and this has been also proven in scientific research and development efforts. But it also comes with some drawbacks. Tungsten, when it reaches 1000 degrees Celsius, it recrystallizes. So we need to find a solution to this and one of the ways to do it is to do particle reinforcement with including oxide and carbide particles into the into the matrix of tungsten. Another way to do this is to actually include tungsten composites with tungsten carbide. And this is a way to get this tungsten carbide particles is by using the carbide precursor synthesis. So when we use this as starting mixture, we use the sintering process by a fast field assisted sintering also known as SPS, which is Park plasma sintering, and we get some consolidation consolidation pallets. The consolidation pallets are then characterized in the in terms of density, phase composition, microstructure, thermo mechanical properties, and so on. So the subject of the research at the institute, what the nanomaterials department does is starting the mixture with tungsten and tungsten carbide, which is the letter of the two things that I suggested in the previous slide. And it uses them to consolidate with fast, it sinters, it makes the pallets, and it also includes some of the variables like sintering temperature and time, and the uniaxial pressure that is applied. The output of the sintering is then the consolidated pallets, which you can see on the third image. And on the fourth image, you can see the microstructural, you actually can't see it, sorry. You can see the structure of the tungsten carbide grains, which are formed in the tungsten boundaries. So these are some experimental results from the department. On the leftmost graph, we can see that at the x-axis, we have the percentage of the carbon, and at the y-axis, we have the concentration of the tungsten carbide. The red dots indicate the experimental results that we had, and the yellow dotted line actually shows the calculated. Yeah, it's okay. Yeah, it's okay. We get the calculated calculations by chemical formulas. So we can see that the experimental results yielded the results that we have lower tungsten concentrations that then we would expect with the calculations. The composition of the subjects also affects some of the mechanical properties, like the structural strength, which is the bending strength, and the hardness of the material. So this is actually the data set that we get at the end. We will come back to it later, I mean, how we used it in the machine learning part, and the green part is actually what we have as a parameter, so the mixture. So we have the applied pressure. We have the height, the density, the diameter, I'm sorry, and the mass of the tungsten and the tungsten carbonate. And then we have the sintering properties that I mentioned some slides before. And at the end, we have the characterizations in blue of the pellets that we get at the end. So the number of samples that were prepared during this research is close to 750. So where does machine learning step in this problem? We can, to put it most simply, we can look at it as a tool to predict the starting composition to help the department in constructing the starting compositions to get a specific result at the end. For example, if they want to achieve higher bending power, or if they want to achieve higher percentages of density. This in turn reduces the number of experiments and it saves time and it saves resources for the department and everyone else. So what we did was implement regression trees and ensembles of regression trees in the form of a random forest. And we did it for a single target prediction and multiple target prediction. And we also did some feature ranking with random forest. Okay. So coming back to the data set, we have independent variables and dependent variables or targets. As a standard supervision task, we are using the independent variables to predict the targets or the dependent variables. In this case, as independent variables, we have the percentage of added carbon. We have the applied pressure, the dimensions of the sample, height, diameter and mass. And we have the sintering related measures that I already talked about. As targets, we have the percentage of theoretical density and the flexural or bending strength of the pallet at the end. So first we did single target prediction, which means that we did separate models for the two targets separately. So on the left side, we can see the prediction for the flexural or bending strength expressed in megapascals. We can see that the carbon percentage was the most important feature here. If we have a percentage higher than 50% for the carbon, then the sigma or the bending strength is the average of the sigma or the bending strength is 1258 megapascals. When predicting the percentage of the theoretical density, the diameter played the pivotal role. When the diameter is bigger than 10.9 millimeters, the percentage of the theoretical density is close to 95%. When it's between 0.95 millimeters and 10.9 millimeters, the percentage is close to 40%. And then when it's below 9.95 millimeters, the percentage is close to 70%. The second thing we did was multi-target prediction, because we have two targets now. I believe the professor talked about it yesterday. So here I won't go into depth in the tree. I mean, we can see that the maximum sintering temperature and the mass and also the carbon percentage play the biggest roles here. And in the notes, we can see that we have predictions for the averages for both targets. These were constructed using PCTs, so not regular regression trees, but predictive clustering trees. I believe, again, that the professor talked about it yesterday, but to refresh your memory, it's essentially considering the decision to your regression tree as a hierarchical clustering system. So at the beginning on the top node, you have the entire dataset. And then as you go down, you recursively get smaller and smaller clusters. And at the end, you get the smallest clusters when you reach the stopping criteria. It was done using one global model for both targets and for building the multi-target regression trees, the class software was used. If you want to play around with it, the link to the software is in the presentation. PCTs are implemented in class plus. And also we can do ensembles and regular single trees. The ensemble model was also developed for multi-target prediction and also for the single-target prediction. Ensembles are essentially a set of base classifiers that all vote to predict a single or multiple targets. So next, we get to the feature ranking. And this was done using the random forest score. So how the random forest score works is essentially it takes one feature and it calculates its predictive power or the error it makes when it predicts the target. And then it permutes it in a way that it adds some noise to the attribute. So then we measure the predictive power on the permuted attribute. And if the predictive power decreases significantly, that means that that attribute has more predictive power and it's supposed to be ranked higher in the entire structure. So this is the formula that we use. Epsilon is the number of trees. The first error is the error that we get on the permuted attribute. And the second error or error out of back for the tree is the error that we get with the original feature. These are the feature rankings for all three models. So the first two represent the single target models for the feature ranking, for bending strength, feature ranking for the percentage of density. And then the third part represents the feature ranking for the multi-target prediction. If you remember when I showed the trees for the feature ranking of bending strength, the carbon percentage was the only one there, which means that it's the most important. The feature ranking for the percentage of density also had the diameter as the most important feature. And the feature ranking for multi-target prediction. If we go back, you can see that the maximum sintering temperature and the mass were one of the highest features. So in conclusion, the results from the machine learning show us that the processing parameters has the strongest influence on the samples, mechanical properties. The diameter of the pallet has the biggest influence on the relative density. And for the flexural, for the bending strength, the carbon percentage was the most important one, which separated data into two clear groups. Thank you. And I will be happy to take any questions. Thank you, Cynthia. Very interesting talk. How about any questions? Okay, here we go. I think Kevin, you have the mic. Thanks for the talk. In the previous slide, you show feature rankings where the carbon percentage is the first on the left-hand side and the third one at the sensor in the sensor pattern. Why does it become the second and not the first when you do the multi-target prediction? Can you explain? Yeah, because this was done for a single target. So we are looking how carbon percentage is affecting the prediction of the bending strength and then the prediction of the density. So we measure the error on different targets. So it is expected to have different rankings. Okay. Thank you for the very nice talk. So how, presumably, you are an expert on these tree methods. So how easy was it for you to take the code that you had and apply it to this dataset? Did you have to adjust it somehow or did it work pretty straightforwardly out of the box? Yeah. Well, by using the class software, it is pretty straightforward because it is already, everything is already generated. You just need to play around with the attributes because it implements the predictive clustering trees. You just need to list the descriptive part and the target part and the clustering part. So you said it was pretty straightforward? Yes. Okay. Any other questions? Good. Then I can ask one. I wanted also to know something related to the software and use of software. So this was a regression problem, right? Yeah. So what kind of quality metric did you use? The Pearson correlation coefficient. Okay. And what were the accuracies that you achieved? Maybe I missed this in the talk. Yeah. So for the bending strength and for the percentage of the density, we got somewhere around 0.6, 0.7 on the test data. So on the training data, it was even higher. And for the multi-target prediction, we got somewhere around 0.7 on the testing data. Okay. So what would be, I mean, is this enough accuracy for the experimentalists? And how would you go about improving the accuracy? Well, yeah, that's kind of a touchy subject. I mean, what's accurate for... Oh, what's enough? Yeah, what's enough, exactly. I mean, especially in the correlation coefficient part. But as I said, the main task here, I mean, the main reason why we were doing machine learning was to help them kind of understand how to set up the initial experiment. So how to set up the mixture, which of the attributes, like for example, they need to pay attention. Now they know that they need to pay attention more maybe to the diameter when predicting higher percentages of the density. Okay, thank you very much. So thank you to all our speakers of the session again. And now we have a coffee break just outside and we'll be back in 20 minutes. So it's a bit of a short coffee break. And we start at 22.4.