Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show that non-sampling-based latent state inference used in HSMM's can be generalized to latent Continuous-Time semi-Markov Chains (CTSMC's). We formulate integro-differential forward and backward equations adjusted to the observation likelihood and introduce an exact integral equation for the Bayesian posterior marginals and a scalable Viterbi-type algorithm for posterior path estimates. The presented equations can be efficiently solved using well-known numerical methods. As a practical tool, variable-step HSMM's are introduced. We evaluate our approaches in latent state inference scenarios in comparison to classical HSMM's

Advancing Machine Learning Algorithms for Object Localization in Data-Limited Scenarios : Techniques for 6DoF Pose Estimation and 2D Localization with limited Data

Recent successes of Machine Learning (ML) algorithms have profoundly influenced many fields, particularly Computer Vision (CV). One longstanding problem in CV is the task of determining the position and orientation of an object as depicted in an image in 3D space, relative to the recording camera sensor. Accurate pose estimation is essential for domains, such as robotics, augmented reality, autonomous driving, quality inspection in manufacturing, and many more. Current state-of-the-art pose estimation algorithms are dominated by Deep Learning-based approaches. However, adoption of these best in class algorithms to real-world tasks is often constrained by data limitations, such as not enough training data being available, existing data being of insufficient quality, data missing annotations, data having noisy annotations, or no directly suitable training data being available at all. This thesis presents contributions on both 6D object pose estimation, as well as on alleviating the restrictions of data limitations, for pose estimation, and for related CV problems such as classification, segmentation, and 2D object detection. It offers a range of solutions to enhance quality and efficiency of these tasks under different kinds of data limitations. The first contribution enhances a state-of-the-art pose estimation algorithm to predict a probability distribution of poses, instead of a single pose estimate. This approach allows to sample multiple, plausible poses for further refinement and outperforms the baseline algorithm even when sampling only the most likely pose. In our second contribution, we drastically improve runtime and reduce resource requirements to bring state-of-the-art pose estimation to low power edge devices, such as modern augmented and extended reality devices. Finally, we extend a pose estimator based on dense-feature prediction to incorporate additional views and illustrate its performance benefits in the stereo use case. The second set of two contributions focuses on data generation for ML-based CV tasks. High quality training data is a crucial component for best performance. We introduce a novel yet simple setup to record physical objects and generate all necessary annotations in a fully automated way. Evaluated on the 2D object detection use case, training on our data performs favourably with more complex data generation processes, such as real-world recordings and physically-based rendering. In a follow-up paper, we further improve upon the results by introducing a novel postprocessing step based on denoising diffusion probabilistic models (DDPM). At the intersection of 6D pose estimation and data generation methods, a final group of three contributions focuses on solving or circumventing the data problem with a range of different approaches. First, we demonstrate the use of physically-based, photorealistic, and non-photorealistic rendering to localize objects on Microsoft HoloLens 2, without needing any real-world images for training. Second, we extend a zero-shot pose estimation method by predicting geometric features, thereby improving estimation quality with almost no additional runtime. Third, we demonstrate pose estimation of objects with unseen appearances based on a 3D scene representation, allowing robust mesh-free pose estimation. In summary, this thesis advances the fields of 6D object pose estimation and alleviates some common data limitations for pose estimation and similar Machine Learning algorithms in Computer Vision problems, such as 2D detection and segmentation. The solutions proposed include several extensions to state-of-the-art 6D pose estimators and address the challenges of limited or poor quality training data, paving the way for more accurate, efficient, and accessible pose estimation technologies across various industries and fields

Moment-Based Variational Inference for Markov Jump Processes

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence from the approximate to the posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to latent parameter inference and demonstrate the method on several examples

Boolean finite cell method for multi-material problems including local enrichment of the Ansatz space

The Finite Cell Method (FCM) allows for an efficient and accurate simulation of complex geometries by utilizing an unfitted discretization based on rectangular elements equipped with higher-order shape functions. Since the mesh is not aligned to the geometric features, cut elements arise that are intersected by domain boundaries or internal material interfaces. Hence, for an accurate simulation of multi-material problems, several challenges have to be solved to handle cut elements. On the one hand, special integration schemes have to be used for computing the discontinuous integrands and on the other hand, the weak discontinuity of the displacement field along the material interfaces has to be captured accurately. While for the first issue, a space-tree decomposition is often employed, the latter issue can be solved by utilizing a local enrichment approach, adopted from the extended finite element method. In our contribution, a novel integration scheme for multi-material problems is introduced that, based on the B-FCM formulation for porous media, originally proposed by Abedian and Düster (Comput Mech 59(5):877–886, 2017), extends the standard space-tree decomposition by Boolean operations yielding a significantly reduced computational effort. The proposed multi-material B-FCM approach is combined with the local enrichment technique and tested for several problems involving material interfaces in 2D and 3D. The results show that the number of integration points and the computational time can be reduced by a significant amount, while maintaining the same accuracy as the standard FCM

Direct observation of the energetics at a semiconductor/liquid junction by operando X-ray photoelectron spectroscopy

Photoelectrochemical (PEC) cells based on semiconductor/liquid interfaces provide a method of converting solar energy to electricity or fuels. Currently, the understanding of semiconductor/liquid interfaces is inferred from experiments and models. Operando ambient-pressure X-ray photoelectron spectroscopy (AP-XPS) has been used herein to directly characterize the semiconductor/liquid junction at room temperature under real-time electrochemical control. X-ray synchrotron radiation in conjunction with AP-XPS has enabled simultaneous monitoring of the solid surface, the solid/electrolyte interface, and the bulk electrolyte of a PEC cell as a function of the applied potential, U. The observed shifts in binding energy with respect to the applied potential have directly revealed ohmic and rectifying junction behavior on metallized and semiconducting samples, respectively. Additionally, the non-linear response of the core level binding energies to changes in the applied electrode potential has revealed the influence of defect-derived electronic states on the Galvani potential across the complete cell

K‐Doping Suppresses Oxygen Redox in P2‐Na₀.₆₇Ni₀.₁₁Cu₀.₂₂Mn₀.₆₇O₂ Cathode Materials for Sodium‐Ion Batteries

In P2‐type layered oxide cathodes, Na site‐regulation strategies are proposed to modulate the Na⁺ distribution and structural stability. However, their impact on the oxygen redox reactions remains poorly understood. Herein, the incorporation of K⁺ in the Na layer of Na₀.₆₇Ni₀.₁₁Cu₀.₂₂Mn₀.₆₇O₂ is successfully applied. The effects of partial substitution of Na⁺ with K⁺ on electrochemical properties, structural stability, and oxygen redox reactions have been extensively studied. Improved Na⁺ diffusion kinetics of the cathode is observed from galvanostatic intermittent titration technique (GITT) and rate performance. The valence states and local structural environment of the transition metals (TMs) are elucidated via operando synchrotron X‐ray absorption spectroscopy (XAS). It is revealed that the TMO₂ slabs tend to be strengthened by K‐doping, which efficiently facilitates reversible local structural change. Operando X‐ray diffraction (XRD) further confirms more reversible phase changes during the charge/discharge for the cathode after K‐doping. Density functional theory (DFT) calculations suggest that oxygen redox reaction in Na₀.₆₂K₀.₀₃Ni₀.₁₁Cu₀.₂₂Mn₀.₆₇O₂ cathode has been remarkably suppressed as the nonbonding O 2p states shift down in the energy. This is further corroborated experimentally by resonant inelastic X‐ray scattering (RIXS) spectroscopy, ultimately proving the role of K⁺ incorporated in the Na layer

Thermodynamically consistent concurrent material and structure optimization of elastoplastic multiphase hierarchical systems

The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose macroscale behavior is governed by their microstructure composition that can evolve over multiple length scales from a few micrometers to centimeters. It is based on the split of the multiscale optimization problem into two nested sub-problems, one at the macroscale (structure) and the other at the microscales (material). In this paper, we establish a novel formulation of concurrent material and structure optimization for multiphase hierarchical systems with elastoplastic constituents at the material scales. Exploiting the thermomechanical foundations of elastoplasticity, we reformulate the material optimization problem based on the maximum plastic dissipation principle such that it assumes the format of an elastoplastic constitutive law and can be efficiently solved via modified return mapping algorithms. We integrate continuum micromechanics based estimates of the stiffness and the yield criterion into the formulation, which opens the door to a computationally feasible treatment of the material optimization problem. To demonstrate the accuracy and robustness of our framework, we define new benchmark tests with several material scales that, for the first time, become computationally feasible. We argue that our formulation naturally extends to multiscale optimization under further path-dependent effects such as viscoplasticity or multiscale fracture and damage

Drying of Soft Colloidal Films

Thin films made of deformable micro‐ and nano‐units, such as biological membranes, polymer interfaces, and particle‐laden liquid surfaces, exhibit a complex behavior during drying, with consequences for various applications like wound healing, coating technologies, and additive manufacturing. Studying the drying dynamics and structural changes of soft colloidal films thus holds the potential to yield valuable insights to achieve improvements for applications. In this study, interfacial monolayers of core‐shell (CS) microgels with varying degrees of softness are employed as model systems and to investigate their drying behavior on differently modified solid substrates (hydrophobic vs hydrophilic). By leveraging video microscopy, particle tracking, and thin film interference, this study shed light on the interplay between microgel adhesion to solid surfaces and the immersion capillary forces that arise in the thin liquid film. It is discovered that a dried replica of the interfacial microstructure can be more accurately achieved on a hydrophobic substrate relative to a hydrophilic one, particularly when employing softer colloids as opposed to harder counterparts. These observations are qualitatively supported by experiments with a thin film pressure balance which allows mimicking and controlling the drying process and by computer simulations with coarse‐grained models

Josef Ganz: Miterfinder des VW Käfers

Bis heute ist der VW Käfer eines der meistverkauften Fahrzeuge der Welt. Als sein Erfinder wird meist Ferdinand Porsche genannt. Die Erfindung des VW Käfers lässt sich aber nicht auf einen einzigen Erfinder festlegen. Josef Ganz, ein Alumnus der Technischen Hochschule Darmstadt, legte durch sein Design und das Konzept eines Prototypen den Grundstein des VW Käfers

From Jean Leray to the millennium problem: the Navier–Stokes equations

One of the Millennium problems of Clay Mathematics Institute from 2000 concerns the regularity of solutions to the instationary Navier–Stokes equations in three dimensions. For an official problem description, we refer to an article by Charles Fefferman (Existence and smoothness of the Navier–Stokes equation. http://www.claymath.org/sites/default/files/navierstokes.pdf) on the whole space problem as well as the periodic setting in ℝ³. In this article, we will introduce the Navier–Stokes equations, describe their main mathematical problems, discuss several of the most important results, starting from 1934 with the seminal work by Jean Leray, and proceeding to very recent results on non-uniqueness and examples involving singularities. On this tour de force we will explain the open problem of regularity