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Type: Text × Subject: Gaussian processes ×

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    Machine learning for additive manufacturing: Predicting materials characteristics and their uncertainty
    (Amsterdam [u.a.] : Elsevier Science, 2023) Chernyavsky, Dmitry; Kononenko, Denys Y.; Han, Jun Hee; Kim, Hwi Jun; van den Brink, Jeroen; Kosiba, Konrad
    Additive manufacturing (AM) is known for versatile fabrication of complex parts, while also allowing the synthesis of materials with desired microstructures and resulting properties. These benefits come at a cost: process control to manufacture parts within given specifications is very challenging due to the relevance of a large number of processing parameters. Efficient predictive machine learning (ML) models trained on small datasets, can minimize this cost. They also allow to assess the quality of the dataset inclusive of uncertainty. This is important in order for additively manufactured parts to meet property specifications not only on average, but also within a given variance or uncertainty. Here, we demonstrate this strategy by developing a heteroscedastic Gaussian process (HGP) model, from a dataset based on laser powder bed fusion of a glass-forming alloy at varying processing parameters. Using amorphicity as the microstructural descriptor, we train the model on our Zr52.5Cu17.9Ni14.6Al10Ti5 (at.%) alloy dataset. The HGP model not only accurately predicts the mean value of amorphicity, but also provides the respective uncertainty. The quantification of the aleatoric and epistemic uncertainty contributions allows to assess intrinsic inaccuracies of the dataset, as well as identify underlying physical phenomena. This HGP model approach enables to systematically improve ML-driven AM processes.
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    Dependence on the dimension for complexity of approximation of random fields
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Serdyukova, Nora
    We consider the $e $-approximation by $n$-term partial sums of the Karhunen-Loève expansion to $d$-parametric random fields of tensor product-type in the average case setting. We investigate the behavior, as $dto infty$, of the information complexity $n(e,d)$ of approximation with error not exceeding a given level $e$. It was recently shown by M. A. Lifshits and E. V. Tulyakova that for this problem one observes the curse of dimensionality (intractability) phenomenon. The aim of this paper is to give the exact asymptotic expression for $n(e,d)$.
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    Soil Nutrient Detection for Precision Agriculture Using Handheld Laser-Induced Breakdown Spectroscopy (LIBS) and Multivariate Regression Methods (PLSR, Lasso and GPR)
    (Basel : MDPI, 2020) Erler, Alexander; Riebe, Daniel; Beitz, Toralf; Löhmannsröben, Hans-Gerd; Gebbers, Robin
    Precision agriculture (PA) strongly relies on spatially differentiated sensor information. Handheld instruments based on laser-induced breakdown spectroscopy (LIBS) are a promising sensor technique for the in-field determination of various soil parameters. In this work, the potential of handheld LIBS for the determination of the total mass fractions of the major nutrients Ca, K, Mg, N, P and the trace nutrients Mn, Fe was evaluated. Additionally, other soil parameters, such as humus content, soil pH value and plant available P content, were determined. Since the quantification of nutrients by LIBS depends strongly on the soil matrix, various multivariate regression methods were used for calibration and prediction. These include partial least squares regression (PLSR), least absolute shrinkage and selection operator regression (Lasso), and Gaussian process regression (GPR). The best prediction results were obtained for Ca, K, Mg and Fe. The coefficients of determination obtained for other nutrients were smaller. This is due to much lower concentrations in the case of Mn, while the low number of lines and very weak intensities are the reason for the deviation of N and P. Soil parameters that are not directly related to one element, such as pH, could also be predicted. Lasso and GPR yielded slightly better results than PLSR. Additionally, several methods of data pretreatment were investigated.