Machine Learning and Deep Learning applications for the protection of nuclear fusion devices

This Thesis addresses the use of artificial intelligence methods for the protection of nuclear fusion devices with reference to the Joint European Torus (JET) Tokamak and the Wendenstein 7-X (W7-X) Stellarator. JET is currently the world's largest operational Tokamak and the only one operated with the Deuterium-Tritium fuel, while W7-X is the world's largest and most advanced Stellarator. For the work on JET, research focused on the prediction of “disruptions”, and sudden terminations of plasma confinement. For the development and testing of machine learning classifiers, a total of 198 disrupted discharges and 219 regularly terminated discharges from JET. Convolutional Neural Networks (CNNs) were proposed to extract the spatiotemporal characteristics from plasma temperature, density and radiation profiles. Since the CNN is a supervised algorithm, it is necessary to explicitly assign a label to the time windows of the dataset during training. All segments belonging to regularly terminated discharges were labelled as 'stable'. For each disrupted discharge, the labelling of 'unstable' was performed by automatically identifying the pre-disruption phase using an algorithm developed during the PhD. The CNN performance has been evaluated using disrupted and regularly terminated discharges from a decade of JET experimental campaigns, from 2011 to 2020, showing the robustness of the algorithm. Concerning W7-X, the research involved the real-time measurement of heat fluxes on plasma-facing components. THEODOR is a code currently used at W7-X for computing heat fluxes offline. However, for heat load control, fast heat flux estimation in real-time is required. Part of the PhD work was dedicated to refactoring and optimizing the THEODOR code, with the aim of speeding up calculation times and making it compatible with real-time use. In addition, a Physics Informed Neural Network (PINN) model was proposed to bring thermal flow computation to GPUs for real-time implementation

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid‐dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Surrogate models for laser powder bed fusion digital twins

Accurate and fast modeling of the temperature distribution and phase transitions in laser powder bed fusion is a major milestone in achieving its quality assurance. Commonly referred to as digital twin technology, the goal is to fi nd agile, fast-to-compute but also sufficiently accurate simulators that can replicate the 3D printing process while enhancing the quality of its outcomes. While the nonlinear heat equation in the context of laser powder bed fusion is numerically solved by the finite element method, three time-efficient surrogates are proposed as fast alternatives with different trade-offs between model accuracy, robustness, offline preparation, and online execution time. The fi rst one is the reduced Gaussian process surrogate, which is a data-driven model equipped with a nonlinear dimension reduction scheme. It outperforms in real-time execution online managing to predict temperature profi les almost instantly, though it is comparably less accurate, not robust to random anisotropy, and requires o ine preparation of data generation, nonlinear dimension reduction, and training. The second one is the sketched surrogate with data-driven local projection. It projects the accurate but high-dimensional nite element method solution with a low-dimensional basis formed by subsampled training temperatures and then bypasses the majority of costly computations for the temperature-dependent matrices in the projected model by randomized sketching. It is the most accurate surrogate while lacking robustness, necessitating the same offline preparation, and taking more time compared with the rst surrogate. The third one is the sketched surrogate with online local projection. Its projection bases are generated in the process of simulation by combining previous temperature pro les and locally deployed anisotropic Gaussian functions, while the sketching process utilizes efficient sampling within out replacement based on approximate optimal sampling distributions. Both the projection and the sketching are designed to implement alongside the printing process, which makes this surrogate capable of handling different process parameters without requiring prior computations offline. The third surrogate, therefore, is accurate, robust, and requires no offline preparation, although it entails longer online execution time compared to the other two surrogates. A series of numerical experiments are carried out to present and compare the performance of the three surrogates, which assumes a two-layer printing process with a fixed laser beam trajectory using different printing attributes (laser power and scan speed) and arbitrary thermal conductivity anisotropy. All three surrogates are also principally feasible in other thermal-driven additive manufacturing to obtain better quality assurance with techniques like uncertainty management and closed-loop control

Proceedings of the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

This book is a collection of 15 reviewed technical reports summarizing the presentations at the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory. The covered topics include image processing, optical signal processing, visual inspection, pattern recognition and classification, human-machine interaction, world and situation modeling, autonomous system localization and mapping, information fusion, and trust propagation in sensor networks

A Bayesian approach to data-driven discovery of nonlinear dynamic equations

Dynamic equations parameterized by differential equations are used to represent a variety of real-world processes. The equations used to describe these processes are generally derived based on physical principles and a scientific understanding of the process. Statisticians have embedded these physically-inspired differential equations into a probabilistic framework, providing uncertainty quantification to parameter estimates and model specification. These statistical models typically rely on a predefined differential equation or class of models to represent the dynamics of the system. Recently, methods have been developed to discover the governing equation of complex systems. However, these approaches rarely account for uncertainty in the discovered equations, and when uncertainty is accounted for, it is not for the complete system. This dissertation begins with a statistical model for the seasonal temperature cycle over North America, where the dynamics of the system are parameterized by a specified functional form. The model highlights how the seasonal cycle is changing in space and time, motivating the need to better understand the driving mechanisms of such systems. Then, a statistical approach to data-driven discovery is proposed, where uncertainty is incorporated throughout the complete modeling process. The novelty of the approach is the dynamics are treated as a random process, which has not be considered previously in the data-driven discovery literature. The proposed approach sits at the junction between the statistical approach of incorporating dynamic equations in a probabilistic framework and the data-driven discovery methods proposed in computer science, physics, and applied mathematics. The proposed method is put into context within the broader literature, highlighting its contribution to the field of data-driven discovery.Includes bibliographical references

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal