# PhD Topics

##### 1. Lensless X-Ray Microscopy at the Photon Limit

Supervisors: Prof. Dr. Christian Schroer (DESY, UHH), Jun.-Prof. Dr. Mathias Trabs (UHH)

The goal of this PhD project is the development and application of denoising and deconvolution techniques to data obtained via different modes of lensless X-ray microscopy. The candidate will be involved in all stages of the data life cycle. This involves the acquisition at the experiment, reconstruction and evaluation of the data. The focus of this project is the improvement of the data reconstruction step. Currently, the reconstruction is carried out by iterative phasing methods which already perform well although the methodology ignores blurring effects and observation noise of the measurements. Taking into account these additional problems, deconvolution and denoising techniques in combination with the state-of-the-art phasing methods should improve the reconstruction of the original signal. For classical statistical (inverse) regression models, there are various deblurring and denoising procedures which are already well understood, including Fourier or spectral methods, non-parametric Bayes methods.

To adapt such methods in the more complex physical context, the present convolution operator has to be understood precisely which then allows for the construction, implementation and application of novel reconstruction methods e.g. statistical multiresolution estimation.

The candidate will integrate these new techniques in the existing workflow and evaluate their capabilities in terms of reconstruction enhancement and applicability to the constantly growing size of data sets. The success of these tests will depend also on the performance of the numerical implementation of the methods under survey. We are looking for a candidate who is interested in different modi of imaging and in applying mathematically and numerical challenging methods to data obtained by these methods.

##### 2. Workflows for reproducible computational science and data science

Supervisors: Prof. Dr. Hans Fangohr (European XFEL), Dr. Sandor Brockhauser (European XFEL), Dr. Adrian Mancuso (European XFEL), Prof. Dr. Volker Guelzow (DESY), Prof. Dr. Thomas Ludwig (UHH)

Carrying out data analysis of scientific data obtained during experiments is a main activity in photon science, and is essential to convert the obtained data into understanding, and eventually publications. A topic that receives growing attention is that of reproducibility and re-usability: Given a publication, it should be possible for readers of the publication to reproduce the results published in the paper, particularly so if the results are based on computational processes. This forms the bases for re-use of the work, for example to extend the analysis software to carry out a related but new study. In practice, this is often impossible. In this project, we will investigate the process of data analysis towards publication and then work to improve this workflow. Typically, data analysis involves processing huge amounts of data (GB to PB) using a range of specialist software tools. Challenges include to preserve all these processing steps, the specialist software, and its computation environment so that the computation can be reproduced and re-used in the future. Objectives are to make the process reproducible, convenient and effective. Important tools for the technical part of this work are likely to include the Jupyter Notebook and an ecosystem of tools, including Python, package managers such as Spack, and containers. We are looking for a computational scientist with a background in physics, chemistry, biology, mathematics, engineering or similar with strong interest in programming and computational science, or for a computer scientist with interest in supporting computational science.

##### 3. Cost-Effective High-Performance Simulation of Next Generation Light Sources

Supervisors: Prof. Dr. Markus Bause (HSU), Prof. Dr. Michael Breuer (HSU), Prof. Dr. Franz Kärtner (CFEL, DESY, UHH), Dr. Jens Osterhoff (DESY)

X-ray Free-Electron Lasers (XFELs) driven by compact electron accelerators and using short period undulators show complex behavior and are extremely challenging to simulate. Some 10 million electrons are involved in a highly nonlinear motion with collective effects driven by electro-magnetic fields ranging from the mm-wavelength range down to the hard-X-ray wavelength range at a fraction of an Angstrom. To understand and optimize X-ray production with these sources asks for an exact simultaneous solution of the emission and motion of electrons and electro-magnetic fields on multiple time and spatial scales. Even though significant progress has been made in the numerical simulation of particle motion under field effects, substantial progress is still required for XFELs. Data mining, in particular machine learning, offers the potential to accelerate computations, such that a real breakthrough becomes feasible, by inferring knowledge from data bases instead of computing all physical quantities of the system on sufficiently fine spatial and temporal scales. By combining the expertise of the involved research groups, the long-term goal is to achieve the simulations only by providing the physics and geometry of the problem, consequently reducing the mesh and solver parameters setup time to almost zero and eliminating the need of expertise. We are looking for one PhD student working on such cost-effective simulations of X-ray sources. Knowledge of numerical approaches for partial differential equations and/or machine learning techniques is desired. Advanced programming skills are mandatory. The student will be supervised conjointly and integrated fully in the research groups with stimulating atmosphere. Excellent equipment is offered by the groups.

##### 4. Scalable in situ visual analytics of multivariate volume data time series for materials science applications

Supervisors: Prof. Dr. Martin Müller (HZG), Prof. Dr. Stephan Olbrich (UHH)

To support materials science applications, we will develop and integrate application-specific data stream and file interfaces as well as processing and visualization algorithms, and optimize them for scalability and usability, based on an existing in-situ parallel data streaming and extraction framework. It is planned to combine and tightly couple 3Dd image based data extraction methods with 3D geometry based analytics, in order to develop and integrate innovative hybrid methods, e. g. for segmentation purposes. These should reduce or avoid intermediate data and take advantage of complexity reduction (O(N3) volume/voxel → O(N2) surface/polygons), in order to efficiently and automatically generate abstractions of the characteristics of materials and its changes over time. To enable and support interdisciplinary usage and openness for scientific and public scenarios, efficient parallel compression and decompression will be integrated as part of the extraction of the resulting 3D geometric and/or symbolic representations, and a thin multi-platform client software will be provided for open access and remote 3D viewing.

##### 5. Phase Retrieval in Imaging and Speech Enhancement

Supervisors: Prof. Dr. Henry Chapman (DESY, CFEL, UHH), Prof. Dr.-Ing. Timo Gerkmann (UHH)

Advanced sources such as free-electron lasers produce intense and coherent beams of X-rays that are opening up new possibilities to image biological materials, such as single molecules, at atomic resolution. Since atomic-resolution lenses do not exist such methods usually rely upon retrieving the structural information encoded in the far-field coherent diffraction pattern [Shechtman et al, 2015]. This intensity pattern corresponds to the Fourier magnitude of the object, and is thus an incomplete measurement since the spectral phase cannot be measured. To reconstruct the original structure, the missing phase information needs to be retrieved . A very similar problem of phase retrieval is encountered in speech source separation and enhancement, which has received increasing attention recently [Gerkmann et al, 2015]. Just in the last few years, modern machine learning methods have been successfully applied to the problem aiming to obtain faster and more accurate results.

The goal of this project is to explore common concepts in X-ray imaging and speech enhancement. Recent advances in the application of machine learning in speech analysis will be transferred and tailored to X-ray imaging, obtaining deeper insights into this challenging inverse problem and providing new opportunities for high-resolution structure determination of biological systems.

##### 6. Dynamic protein pattern Recognition In Free-Electron Laser Experiments

Supervisors: Dr. Sadia Bari (DESY), Prof. Dr. Simone Techert (DESY), Jun.-Prof. Dr. Robert Meißner (TUHH, HZG)

Utilizing the unique pulsed features of x-ray free-electron laser (FELs), it will become possible not only to study the structure of radiation sensitive and fragile proteins as well as complexes, but also to gain a deeper understanding of their dynamics. Going beyond well-ordered systems, it is expected that the combination of x-ray scattering and x-ray spectroscopy methods combined with advanced molecular dynamics (MD) simulations leads to real-time dynamics information about molecular migration and overall structural dynamics information of protein entities. Investigated mechanisms include folding-unfolding processes, protein aggregation or segregation as well as dynamics of intrinsically disordered proteins. Machine learning approaches, e.g. pattern recognition algorithms will be used to identify energetically stable patterns in the conformational space – allowing in combination with x-ray experiments deeper insights into the conformational space of proteins. Mathematical tools based on a probabilistic analysis of molecular motifs and kernel ridge regression techniques are used to determine the fingerprint of biomolecular conformations combining data from advanced MD simulations, online databases and x-ray spectroscopy data. This graduate school provides a unique opportunity to develop and optimize theoretical predictions and simulation algorithms utilizing the provided FEL and synchrotron based spectroscopic data – from small peptides up to hierarchically built-up proteins.

##### 7. Using Prior Knowledge for the Solution of Ill-Posed Inverse Problems in X-Ray Microscopy

Supervisors: Prof. Dr. Christian Schroer (DESY, UHH), Prof. Dr.-Ing. Tobias Knopp (TUHH)

The interpretation of most experimental data in X-ray microscopy requires solving an inverse problem, i. e., finding the physical properties of a sample from a more or less known model for the image formation. Solving such inverse problems is usually a challenging task since the underlying mathematical problem is ill-posed and in turn small perturbations in the measurement due to noise lead to large errors in the calculated solution of the inverse problem. To handle inverse problems, the underlying linear reconstruction problem has to be solved by applying prior knowledge. For instance it can be assumed that the solution is smooth or that it has minimal total variation. In the recent years, the classical solvers for inverse problems have been complemented by approaches that are based on machine learning. Based on large databases of typical images, the inverse imaging operator can be learned and efficiently evaluated. Within this project the goal is to implement, improve, and compare state-of-the art algorithms for the solution of the inverse problem in X-ray microscopy using real-world data. The algorithms will be benchmarked with respect to noise reduction and reconstruction speed. A major focus will be put investigation of artifacts that appear when the algorithms are applied to unusual but physically plausible data.

##### 8. Modeling x-ray superfluorescence by stochastic differential equations

Supervisors:** **Prof. Dr. Nina Rohringer (DESY, UHH), Dr. Andrei Benediktovitch (DESY), ** **Jun.-Prof. Dr. Mathias Trabs (UHH)

We propose an interdisciplinary project between the natural and mathematical sciences to develop a theoretical description of x-ray collective spontaneous emission (superfluorescence and superradiance) in terms of stochastic differential equations with subsequent applications to experimental data. In experiments performed at modern x-ray sources, such as x-ray free electron lasers (XFEL), matter can be driven into highly excited states, where population inversion is created between valence and inner-core electronic shells, or on nuclear resonances. The ensuing short-wavelength emission of such a highly excited system will be of collective nature and exhibits unique properties. It combines the microscopic, quantum mechanical origin of the emission process with a macroscopically large number of ultimately emitted photons. The theoretical description of superfluorescence/superradiance is challenging and so far poorly developed – especially for the x-ray domain. We propose to address this open problem based on the mathematical formalism of stochastic differential equations (SDE). More precisely, the solution of the underlying Fokker-Planck equation can be equivalently characterized as the distribution of the solution process of a SDE. Based on that simple observation, x-ray superfluorescence can be described via stochastic ordinary or partial differential equations that can be studied using tools from stochastic analysis. The developed theory will be verified against data from previous and future measurements at various XFEL sources and samples. In particular, it will be applied to investigate coherence and quantum properties of superfluorescent/superradiant radiation. This may pave the way for novel spectroscopic and/or imaging applications at XFEL that can benefit from the unique properties of the radiation.

##### 9. Quantum Explorer - Pioneering Quantum Computing for Particle Physics and Computer Science

Supervisors: Prof. Dr. Kerstin Borras (DESY / RWTH Aachen), Prof. Dr.- Ing. Matthias Riebisch

Quantum Explorer - Pioneering Quantum Computing for Particle Physics and Computer Science This Computer Science project embarks on the novel and emergent technology of Quantum Computing and Simulations. Pioneering ways to open this cutting-edge technology for solving problems which are presently inaccessible with classical computations is the ultimate goal. The use cases employ Particle Physics questions such as the nature of the early Universe and processing of large data sets. Computational, mathematical and technological challenges arise through the pioneering employment of Quantum Computer Simulations. The project will explore Quantum Simulations by designing optimal Quantum Circuits: development, modelling, simulation and the optimization of their parameters. The produced methods will be implemented on various Quantum Computer platforms such as Rigetti, IBMQ, Google and D-WAVE. Through hands-on experience, a test of these new methods and a comparison of the employed architectures can be achieved. In the PhD project, benchmarks will be developed, optimization methods adapted and applied with the aim of parameterization and the optimization of the Quantum Circuits. In combining the competencies of the collaborators: already performed initial Quantum Simulations, applied Deep Learning and Simulation methods in Particle Physics and expertise in Software Engineering, the project will have strongest impact, advance the research fields and will accomplish a leading role in Quantum Computing.

##### 10. Model based simulation of dynamics in ferromagnetic nanostructures

Supervisors: Prof. Dr. Ralf Röhlsberger (DESY), PD. Dr. Guido Meier (MPSD), Jun.- Prof. Christina Brandt (UHH)

The exact tailoring of magnetic spin systems in thin films and nanostructures plays an important role for designing micromagnetic devices with customized responses to highfrequency fields ranging from the GHz to the THz regime. Fundamental as well as application-directed research in this field is needed to achieve significant advances in highspeed information processing via the spin degree of freedom in magnetic nanostructures. In this project we will join forces in the fields of high-frequency magnetic dynamics (G. Meier), model-based simulation and identification of magnetic spin structures (C. Brandt) and synchrotron radiation methods for determination of static and dynamic magnetic structures (R. Röhlsberger) to explore new regimes in the field of ultrafast dynamics in finite spin systems.

##### 11. Advanced Simulation Methodology for Optimizing Aerodynamic Lenses used for Single-Particle Diffractive Imaging

Supervisors: Prof. Dr. Michael Breuer (HSU), Dr. Philipp Neumann (HSU), Prof. Dr. Jochen Küpper (CFEL, DESY, UHH), Dr. Muhamed Amin (CFEL, DESY)

Single-particle diffractive imaging (SPI) relies on high-density streams of individual aerosolized particles to collect sufficient numbers of diffraction patterns with short x-ray pulses. As the intense xray pulses destroy the intercepted particles, a constant, focused stream of particles is decisive for the recording of many high-quality diffraction patterns. Aerodynamic lens stacks (ALS), a series of orifices, are a widespread technique for obtaining collimated particle beams in SPI experiments, but optimization for certain parameter sets, e.g., particle sizes, flow rates, pressures, is difficult. The development of advanced aerosol injection techniques for better selectivity of the injection and particle control exploiting novel operation regimes, including very low temperatures is thus an important issue. Numerical simulations are an important tool to better understand and optimize ALS, guiding experimental optimization of the injection process. Due to the multiscale character and the wide range of flow states, e.g., continuum vs. free molecular regime, these calculations require advanced simulation methodologies and high-performance computing techniques. Multiscale and multiphysics simulations for a huge number of particles over a large phase space lead to a vast amount of data requiring efficient simulation as well as on-line and off-line data analysis. Simulations of actual experiments on the fluid-dynamic transport and manipulation of nanoparticles/biomolecules over wide ranges of temperatures (4–300 K) and particle sizes (3–300 nm) will utilize particle methods such as molecular dynamics and direct simulation Monte Carlo methods to solve the Boltzmann equation for finite Knudsen numbers Kn; new and more appropriate modeling assumptions will be derived. Further challenges include calculations of actual cooling rates/temperatures of particles in the cold-gas fields and additional simultaneous forces on the particles, e.g., external electric fields, requiring variable multiphysics approaches.

##### 12. Water and Hydrocarbons in Confined Geometries: Correlating High Resolution X-ray Diffraction with Molecular Dynamics Simulation Data

Supervisors: Prof. Dr. Patrick Huber (TUHH), Prof. Dr. Robert Meißner (TUHH), Dr. Oliver Seeck (DESY), Prof. Dr. Marko Lindner (TUHH)

Spatial confinement affects the properties of matter often markedly. For example entirely novel structures and dynamics have been found for water and hydrocarbons in nanoporous media. Such confinements effects play a pivotal role in a huge variety of natural and technological processes, ranging from frost heave and cloud nucleation to transport in biological tissues and catalysis. X-ray scattering is particularly suitable to unravel the complexity of matter in such restricted geometries and Molecular Dynamics (MD) simulations can nowadays provide atomistic information on these nanoscale systems. However, both approaches produce immense data sets and the extraction of appropriate data descriptors as well as the comparison between experiment and simulation is conceptionally very demanding and time consuming. Thus, this project aims at bridging the gap between MD simulation of such confined systems and X-ray scattering experiments, in particular small- and wide-angle diffraction studies at modern X-ray sources. Specifically, machine learning methods shall be employed to identify characteristic patterns in reciprocal space and to link this information with similarly large MD data sets in direct space. Hence, this project on the structure of confined water and hydrocarbons has a particularly interdisciplinary character linking modern experimental and theoretical condensed-matter research with state-of-the-art materials and data science.

##### 13. Adaptive machine learning approximations for quantum simulations of hydrogen bond dynamics

Supervisors: Prof. Dr. Jochen Küpper (CFEL, DESY, UHH), Dr. Andrey Yachmenev (CFEL, DESY), Prof. Dr. Armin Iske (UHH)

First principles simulations of the hydrogen-bond dynamics in molecular complexes with water is one of the most interesting, computationally challenging, and accuracy demanding problems in the field of computational physics and chemistry. Accurate simulations of molecular and chemical dynamics in weakly-bound complexes with water will help to advance our understanding of many organic and biochemical processes. The development of rigorous variational approaches to nuclear motion dynamics of polyatomic molecules enables the accurate theoretical modeling of simple cluster systems. However the exponential scaling of the computational burden with the number of degrees of freedom, i.e., cluster size, renders the computational costs of existing variational methods unaffordable for clusters composed of more than two molecules. The goal of this project is to explore and implement the paradigm of machine-learning to mitigate or break the curse of dimensionality in variational calculations of larger clusters. We are looking for a computational scientist with an interest in physics and mathematics, or a physicist with a background in computer science. Candidates should have experience with quantum mechanics, numerical linear algebra, machine-learning, and programming in Python as well as low-level programming languages such as C/C++/Fortran.

##### 14. Mixed Reality User Interfaces for Operating Particle Accelerators and Laser Facilities

Supervisors: Prof. Dr. Frank Steinicke (UHH), Dr. Wim Leemans (DESY, M – Division Leader), Dr. Reinhard Bacher (DESY)

Modern particle accelerators or laser facilities are fairly complex research facilities producing a huge amount of operations and scientific data. While there is huge interest in developing data science methods to process this enormous amount of data, the underlying physical principles and the inherent complexity of the technical systems involved make the operation and maintenance of these facilities an enormous data science challenge itself. Today, operations are performed through traditional standard user interfaces (UI) providing limited performance for handling complex control and operation tasks. In the proposed thesis, the candidate will explore novel forms of UIs to improve the operation of particle accelerators or laser facilities, in particular, by using mixed reality (MR) technologies such as virtual and augmented reality and three-dimensional (3D) spatial UIs. These novel MR-based UIs will be analyzed, designed implemented and evaluated in a human-centered design (HCD) process including domain experts and laboratory as well as field studies in particle accelerators and laser facilities.

##### 15. Phase and Attenuation Retrieval for Propagation-Based Phase Contrast X-Ray Tomography

Supervisors: Prof. Dr. Martin Müller (HZG), Julian Moosmann (HZG), Prof. Dr.-Ing. Timo Gerkmann (UHH)

Propagation-based phase contrast in near- and full-field X-ray imaging typically assumes the attenuation of X-rays transmitted by the sample to be negligible. However, most samples fulfill this condition only approximately due to residual absorption. Moreover, enhanced intensity contrast due to free-space propagation is beneficial for samples where absorption contrast is low or noisy or for samples which exhibit mixed contrast and where the soft tissue components require additional contrast enhancement such that their signal rises above the absorption signal of the surrounding material. Apart from certain approximations (small phase variations, small attenuation, small propagation distances, attenuation-phase duality), a direct algebraic inversion of the general problem as described by the Fresnel diffraction integral does not exist. For in situ or in vivo experiments, where deposited dose and/or scan time are critical, the acquisition of a second intensity measurement (at a different propagation distance or energy) is not feasible. For such experiments the inverse problem is ill-posed as phase and attenuation have to be reconstructed from a single measurement. The problem is related to phase retrieval in speech enhancement, where in the last few years machine learning techniques have been employed to considerably push the field forward. In this project, expertise in speech enhancement and X-ray tomography are combined to make improvements in both fields.