„… 107 Chapter 6Conclusions 108 Chapter 6 Conclusions Throughout this thesis, the topic of stochastic …” „… stochastic inference in PGMs towards novel methods for generating more efficient particle proposals. This …” „… topic is of particular interest, since the particle proposal generation process is a cruicial part in …”

„… 56 Chapter 4Stochastic Inference in Probabilistic Graphical Models 57 In recent years, stochastic …” „… approach combining stochastic methods with message passing schemes [62, 61]. The particle belief …” „… the sum-product particle belief 58 Chapter 4 Stochastic Inference in Probabilistic Graphical Models x3 …”

„… approximation of the underlying true creation process. All these factors induce uncertainty to the inference …” „… process. Uncertainty can be modeled via the introduction of probabilities. The probabilistic counterpart …” „… wasted in the (often much larger) regions of low probability. In this thesis, stochastic inference …”

„… the idea of MCMC sampling. A Markov chain is a special case of a stochastic process. More precisely …” „… stochastic methods for inference with continuous variables in Section 3.4 and its application on …” „… ). A random variable associates each outcome of a random process to a value (or configuration), denoted …”

„… process simulations. Weimar Optimization and Stochastic Days. 2012 [SWR13] Schimmelpfennig, M …” „… Rooij, R.; Schoofs, A.; Rooda, J.: Simulation based optimization of stochastic systems with integer …” „… destributional laws of stresses in polycristals. Mathematical modeling of systems and processes. 1995. [ATL99 …”

„… process. In contrast to this, methods of design optimization aim at finding the best design parameters in …” „… of constraints. Modern product-development processes use computational design and engineering tools …” „… number of costly prototypes and an overall acceleration of the development processes. Tools, such as …”

„… developmental process, due to their pronounced similarity to cellular automata. However, computational steps of …” „… for topology optimization and a developmental process that is influenced by environmental information …” „… related to modelling the gradient of the objective function. Assuming a suitable learning process, we …”

„… stochastic optimization methods. The chapter is finalized with a summary in Sec. 2.4. 2.1 Background …” „… structure. Sizing and shape optimization are commonly applied relatively late in the design process, when a …” „… introducing topological changes in the structural optimization process. This problem marked starting point for …”

„… process only generates connected structures and crossover and mutation to the cost variables with a …” „… rules or development processes that create the structure, are often inspired by onto- or morphogenesis …” „… processes in nature and mimic various aspects at different levels of abstraction. 3.4.1 Lindenmayer System …”

„… . Response surface methodology: process and product optimization using designed experiments, volume 705. John …” „… Bibliography [175] Spall, J. C. Introduction to stochastic search and optimization: estimation, simulation, and …” „… process. PhD thesis, University of Notre Dame, 2004. [191] Tovar, A., Patel, N. M., Niebur, G. L., Sen, M …”

„… gradients are available. Concretely, the idea of the proposed method is to utilize a learning process that …” „… formulations need to be found externally to the optimization process. One one hand, the advantage of this …” „… process is that an accurate search direction is provided. On the other hand, the problem here is obviously …”

„… different random seeds. As can be expected for algorithms with stochastic components, there is variance in …” „… account for the stochastic nature of the sampling 102 5 Studies on the Minimum Compliance Problem choice …” „… . Similar to the strain energy density, stresses or strains, these LSFs implicitly process the information …”

„… Surrogate modelling for finite element simulations Towards a stochastic surrogate approach B.P …” „… surrogate modelling, a stochastic weight assembly is introduced to the well-known traditional long …” „… VDI-Berichte Nr. 2407, 2022 555 be found by representing the weights in a stochastic sense and subsequently …”

„… development process in automotive engineering, design and production data are generated. In addition …” „… : Applied Stochastic Models in Business and Industry, 22:5-6, 2006, S.431-444 VDI-Berichte Nr. 2407, 2022168 …”

„… Prozessindustrie Material Tracking based Soft Sensor for Greenhouse Gas Emission Monitoring in Process Industries …” „… Process Industries, Cottbus Kurzfassung Die Treibhausgasemissionen (GHG, engl. Greenhouse Gas) sind …” „… requires fine grained process information. In this study, we propose to build a data-driven soft sensor …”

„… (precipitation) is of stochastic nature. On the other hand, dynamic control of the flow processes in the sewer …” „… ), processes are highly distributed and nonlinear (systems of partial differential equations) and system input …” „… integration of an arbitrary internal process model („Digital Twin“) into a model-based predictive control …”