Predicting permeability via statistical learning on higher-order microstructural information

Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that neural networks are superior to the more conventional regression methods for establishing quantitative structure-property relationships

Overparameterized random feature regression with nearly orthogonal data

We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime, where the width of the first layer is much larger than the sample size. Our analysis shows high-probability non-asymptotic concentration results for the training errors, cross-validations, and generalization errors of RFRR centered around their respective values for a kernel ridge regression (KRR). This KRR is derived from an expected kernel generated by a nonlinear random feature map. We then approximate the performance of the KRR by a polynomial kernel matrix obtained from the Hermite polynomial expansion of the activation function, whose degree only depends on the orthogonality among different data points. This polynomial kernel determines the asymptotic behavior of the RFRR and the KRR. Our results hold for a wide variety of activation functions and input data sets that exhibit nearly orthogonal properties. Based on these approximations, we obtain a lower bound for the generalization error of the RFRR for a nonlinear student-teacher model.Comment: 39 pages. A condition on the activation function is added in Assumption 2.

Design optimisation of a funnel-shaped floating dock for installation of offshore wind turbines

Master's thesis in Civil and structural engineering (BYG508)Offshore wind power is a rapidly growing renewable energy industry and has a tremendous potentialof further expansion. Installation of offshore wind turbines is a challenging task. Floating windturbines are believed to be cost-effective solutions for deep water installation. This technologyis extremely sensitive to wave excitation during the installation process. As deep-water windfarms often are located in areas exposed to rough weather, innovative methods of installation areinvestigated. The floating dock concept has been proposed in recent studies in order to expand theweather window for installing spar floating wind turbines. The idea is for the dock to shield the sparfrom wave excitation. Previous studies show that a funnel-shaped dock potentially has a betterhydrodynamic performance compared to cylindrical and bottle-shaped docks. This master’s thesistakes the previous studies into consideration and investigates how a parametric design optimisationcan be carried out for a funnel-shaped dock intended for installation of floating wind turbines. Theoptimisation objective is defined as reduction of steel weight. While investigating how to bestpredict the operational constraint of piston-mode periods, the Gaussian process regression modelappeared to be the best predictor. The study revealed that the heights;T1,T2andT3, in additionto the diameters,Di1andDi2, are design parameters which significantly affect the piston-modeperiod. The optima found in this study deviate from the predictions from the GPR based model asthe geometry is outside the trained model-area. This can be solved with a new model which alsoincludes bottle-shaped and cylindrical docks