Abstract: Random media and the process-structure-property chain generally define complex, high-dimensional and stochastic materials systems, posing a challenging setting for any prediction or optimization task. In this thesis, we pursue a Bayesian approach for learning and predicting the behavior… [weiterlesen]

Abstract: Solving high-dimensional, nonlinear systems is a key challenge in engineering and computational physics. We propose novel physics-aware machine learning models that rely both on physical knowledge as well as a small amount of data and are, after an initial training phase, able to solve… [weiterlesen]

Deep Operator Networks (DeepONets) offer a powerful, data-driven tool for solving parametric PDEs by learning operators, i.e. maps between infinite-dimensional function spaces. In this work, we employ physics-informed DeepONets in the context of high-dimensional, Bayesian inverse problems.… [weiterlesen]

While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials’ community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources and their quantification and integration in the inversion… [weiterlesen]

Abstract: Primary production of metallic iron accounts for a significant share of the industrial green- house gas emissions, and an expected growth in the demand for steel motivates the search for alternative sustainable ways of iron ore reduction. Hydrogen-based direct reduction is a very… [weiterlesen]

Abstract: In recent years, data-driven approaches have significantly reduced the computational effort required to capture the structure-property linkages in high-contrast microstruc- tures. Convolutional neural networks (CNNs), a special form of artificial neural networks (ANNs), have been shown to… [weiterlesen]

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Abstract: The thesis on hand deals with the implementation and investigation of the APHINITY frame- work proposed by Gallinari et al. [24]. The framework provides an unique decomposition of a complex dynamical system into a model based part and into an augmenting machine learn- ing part. While the… [weiterlesen]

Abstract: The simulation of electromagnetic phenomena in geophysical applications has benefited from the continued evolution of computers and numerical methods. However, despite the great success that high-order methods experienced in other engineering fields over the last decades, their… [weiterlesen]