Effizienzsteigernde Methoden haben die Aufgabe, die Rechenzeit von Monte Carlo Simulationen zur Lösung von Strahlungstransportproblemen zu verringern. Dazu gehören weitergehende Quell- oder Geometrievereinfachungen und die Gewichtsfenstertechnik als wichtigstes varianzreduzierendes Verfahren, entwickelt in den 1950er Jahren. Die Schwierigkeit besteht bis heute in der Berechnung geeigneter Gewichtsfenster. In dieser Arbeit wird ein orts- und energieabhängiger Gewichtsfenstergenerator basierend auf dem vorwärts-adjungierten Generator von T.E. BOOTH und J.S. HENDRICKS für das Strahlungstransportprogramm AMOS entwickelt und implementiert. Dieser ist in der Lage, die Gewichtsfenster sowohl iterativ zu berechnen und automatisch zu setzen als auch, deren Energieeinteilung selbstständig anzupassen. Die Arbeitsweise wird anhand des Problems der tiefen Durchdringung von Photonenstrahlung demonstriert, wobei die Effizienz um mehrere Größenordnungen gesteigert werden kann. Energieabhängige Gewichtsfenster sorgen günstigstenfalls für eine weitere Verringerung der Rechenzeit um etwa eine Größenordnung. Für eine praxisbezogene Problemstellung, die Bestrahlung eines Personendosimeters, kann die Effizienz hingegen bestenfalls vervierfacht werden. Quell- und Geometrieveränderungen sind gleichwertig. Energieabhängige Fenster zeigen keine praxisrelevante Effizienzsteigerung.:1 Einleitung 2 Theoretische Grundlagen 2.1 Strahlungsfeldgrößen und Strahlungstransportgleichung 2.2 Monte Carlo Methoden 2.3 Effizienzsteigernde Methoden 3 Gewichtsfenstergenerator 3.1 Güte der Ergebnisse 3.2 Iterative Berechnung 3.3 Implementation in AMOS 4 Anwendungsbeispiele 4.1 Tiefe Durchdringung von Photonenstrahlung 4.2 Gestreute Photonenstrahlung 5 Zusammenfassung und Ausblick 6 Literatur Anhänge / The purpose of efficiency increasing methods is the reduction of the computing time required to solve radiation transport problems using Monte Carlo techniques. Besides additional geometry manipulation and source biasing this includes in particular the weight windows technique as the most important variance reduction method developed in the 1950s. To date the difficulty of this technique is the calculation of appropriate weight windows. In this work a generator for spatial and energy dependent weight windows based on the forward-adjoint generator by T.E. BOOTH and J.S. HENDRICKS is developed and implemented in the radiation transport program AMOS. With this generator the weight windows are calculated iteratively and set automatically. Furthermore the generator is able to autonomously adapt the energy segmentation. The functioning is demonstrated by means of the deep penetration problem of photon radiation. In this case the efficiency can be increased by several orders of magnitude. With energy dependent weight windows the computing time is decreased additionally by approximately one order of magnitude. For a practice-oriented problem, the irradiation of a dosimeter for individual monitoring, the efficiency is only improved by a factor of four at best. Source biasing and geometry manipulation result in an equivalent improvement. The use of energy dependent weight windows proved to be of no practical relevance.:1 Einleitung 2 Theoretische Grundlagen 2.1 Strahlungsfeldgrößen und Strahlungstransportgleichung 2.2 Monte Carlo Methoden 2.3 Effizienzsteigernde Methoden 3 Gewichtsfenstergenerator 3.1 Güte der Ergebnisse 3.2 Iterative Berechnung 3.3 Implementation in AMOS 4 Anwendungsbeispiele 4.1 Tiefe Durchdringung von Photonenstrahlung 4.2 Gestreute Photonenstrahlung 5 Zusammenfassung und Ausblick 6 Literatur Anhänge

<div>The rise of artificial intelligence (AI) hinges on the efficient training of modern deep neural networks (DNNs) for non-convex optimization and uncertainty quantification, which boils down to a non-convex Bayesian learning problem. A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical guarantees. However, non-convex Bayesian learning in real big data applications can be arbitrarily slow and often fails to capture the uncertainty or informative modes given a limited time. As a result, advanced techniques are still required.</div><div><br></div><div>In this thesis, we start with the replica exchange Langevin Monte Carlo (also known as parallel tempering), which is a Markov jump process that proposes appropriate swaps between exploration and exploitation to achieve accelerations. However, the na\"ive extension of swaps to big data problems leads to a large bias, and the bias-corrected swaps are required. Such a mechanism leads to few effective swaps and insignificant accelerations. To alleviate this issue, we first propose a control variates method to reduce the variance of noisy energy estimators and show a potential to accelerate the exponential convergence. We also present the population-chain replica exchange and propose a generalized deterministic even-odd scheme to track the non-reversibility and obtain an optimal round trip rate. Further approximations are conducted based on stochastic gradient descents, which yield a user-friendly nature for large-scale uncertainty approximation tasks without much tuning costs. </div><div><br></div><div>In the second part of the thesis, we study scalable dynamic importance sampling algorithms based on stochastic approximation. Traditional dynamic importance sampling algorithms have achieved successes in bioinformatics and statistical physics, however, the lack of scalability has greatly limited their extensions to big data applications. To handle this scalability issue, we resolve the vanishing gradient problem and propose two dynamic importance sampling algorithms based on stochastic gradient Langevin dynamics. Theoretically, we establish the stability condition for the underlying ordinary differential equation (ODE) system and guarantee the asymptotic convergence of the latent variable to the desired fixed point. Interestingly, such a result still holds given non-convex energy landscapes. In addition, we also propose a pleasingly parallel version of such algorithms with interacting latent variables. We show that the interacting algorithm can be theoretically more efficient than the single-chain alternative with an equivalent computational budget.</div>