Given a population contact network and electronic medical records of patients, how to distribute vaccines to individuals to effectively control a flu epidemic? Similarly, given the Twitter following network and tweets, how to choose the best communities/groups to stop rumors from spreading? How to find the best accounts that bridge celebrities and ordinary users? These questions are related to diffusion (aka propagation) phenomena. Diffusion can be treated as a behavior of spreading contagions (like viruses, ideas, memes, etc.) on some underlying network. It is omnipresent in areas such as social media, public health, and cyber security. Examples include diseases like flu spreading on person-to-person contact networks, memes disseminating by online adoption over online friendship networks, and malware propagating among computer networks. When a contagion spreads, network structure (like nodes/edges/groups, etc.) plays a major role in determining the outcome. For instance, a rumor, if propagated by celebrities, can go viral. Similarly, an epidemic can die out quickly, if vulnerable demographic groups are successfully targeted for vaccination. Hence in this thesis, we aim to optimize and understand network structure better in light of diffusion. We optimize graph topologies by removing nodes/edges for controlling rumors/viruses from spreading, and gain a deeper understanding of a network in terms of diffusion by exploring how nodes group together for similar roles of dissemination. We develop several novel graph mining algorithms, with different levels of granularity (node/edge level to group/community level), from model-driven and data-driven perspectives, focusing on topics like immunization on networks, graph summarization, and community detection. In contrast to previous work, we are the first to systematically develops more realistic, implementable and data-based graph algorithms to control contagions. In addition, our thesis is also the first work to use diffusion to effectively summarize graphs and understand communities/groups of networks in a general way. 1. Model-driven. Diffusion processes are usually described using mathematical models, e.g., the Independent Cascade (IC) model in social media, and the Susceptible-Infectious-Recovered (SIR) model in epidemiology. Given such models, we propose to optimize network structure for controlling propagation (the immunization problem) in several practical and implementable settings, taking into account the presence of infections, the uncertain nature of the data and group structure of the population. We develop efficient algorithms for different interventions, such as vaccination (node removal) and quarantining (edge removal). In addition, we study the graph coarsening problem for both static and temporal networks to obtain a better understanding of relations among nodes when a contagion is propagating. We seek to get a much smaller representation of a large network, while preserving its diffusive properties. 2. Data-driven. Model-driven approaches can provide ideal results if underlying diffusion models are given. However, in many situations, diffusion processes are very complicated, and it is challenging or even impossible to pick the most suited model to describe them. In addition, rapid technological development has provided an abundance of data such as tweets and electronic medical records. Hence, in the second part of the thesis, we explore data-driven approaches for diffusion in networks, which can directly work on propagation data by relaxing modeling assumptions of diffusion. To be specific, we first develop data-driven immunization strategies to stop rumors or allocate vaccines by optimizing network topologies, using large-scale national-level diagnostic patient data with billions of flu records. Second, we propose a novel community detection problem to discover "bridge" and "celebrity" communities from social media data, and design case studies to understand roles of nodes/communities using diffusion. Our work has many applications in multiple areas such as epidemiology, sociology and computer science. For example, our work on efficient immunization algorithms, such as data-driven immunization, can help CDC better allocate vaccines to control flu epidemics in major cities. Similarly, in social media, our work on understanding network structure using diffusion can lead to better community discovery, such as finding media accounts that can boost tweet promotions in Twitter. / Ph. D. / In public health, how to distribute vaccines to effectively control an epidemic like flu over population? In social media, how to identify different roles of users who participate in the spread Of content through social networks? These questions and many others are related to diffusion (aka propagation) phenomena in networks (aka graphs). Networks, as natural structures to model relations between objects, arise in many areas, such as online social networks, population contact network, and the Internet. Diffusion can be treated as a behavior of spreading contagions (like viruses, ideas, memes, etc.) on some underlying network. It is also prevalent: e.g., diseases like flu spreading on person-to-person contact networks, memes disseminating by online adoption over online friendship networks, and malware propagating among computer networks. When a contagion spreads, network structure (like nodes/edges/groups, etc.) plays a major role in determining the outcome. For instance, a rumor, if propagated by celebrities, can go viral. Similarly, an epidemic can die out quickly, if vulnerable demographic groups are successfully targeted for vaccination. This thesis targets at general audience and provides a comprehensive study on how to optimize and understand network structure better in light of diffusion. We optimize graph topologies by removing nodes/edges for controlling rumors/viruses from spreading, and gain a deeper understanding of a network in terms of diffusion by exploring how nodes group together for similar roles of dissemination. In contrast to previous work, we are the first to systematically develops more realistic, implementable and data-based graph algorithms to control contagions. In addition, our thesis is also the first work to use diffusion to effectively summarize graphs and understand communities/groups of networks in a general way. Our work has many applications in multiple areas such as epidemiology, sociology and computer science. For example, our work on efficient immunization algorithms, such as data-driven immunization, can help experts better allocate vaccines to control flu epidemics. Similarly, in social media, our work on understanding network structure using diffusion can lead to better community discovery, such as finding media accounts that can boost tweet promotions in Twitter.

Accelerating physics-based simulations has been an evergreen topic across different scientific communities. This dissertation is devoted to this subject addressing bottlenecks in state-of-the-art approaches to the simulation of fluids of large-scale scenes, viscous threads, magnetic fluids, and the simulation of fibers and thin structures. The contributions within the thesis are rooted in mathematical modeling and numerical simulation as well as in machine learning. The first part deals with the simulation of incompressible flow in a multigrid fashion. For the variational viscous equation, geometric multigrid is inefficient. An Unsmoothed Aggregation Algebraic Multigrid method is devised with a multi-color Gauss-Seidel smoother, which consistently solves this equation in a few iterations for various material parameters. This framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow. In the second part, a new physical model is devised to accelerate the macroscopic simulation of magnetic fluids. Previous work is based on the classical Smoothed-Particle Hydrodynamics (SPH) method and a Kelvin force model. Unfortunately, this model results in a force pointing outwards causing significant levitation problems limiting the application of more advanced SPH frameworks such as Divergence-Free SPH (DFSPH) or Implicit Incompressible SPH (IISPH). This shortcoming has been addressed with this new current loop magnetic force model resulting in more stable and fast simulations of magnetic fluids using DFSPH and IISPH. Following a different trajectory, the third part of this thesis aims for the acceleration of iterative solvers widely used to accurately simulate physical systems. We speedup the simulation for rod dynamics with Graph Networks by predicting the initial guesses to reduce the number of iterations for the constraint projection part of a Position-based Dynamics solver. Compared to existing methods, this approach guarantees long-term stability and therefore leads to more accurate solutions.

In autonomous driving, scenario generation can play a critical role when it comes to the verification of the autonomous driving software. Since uncertainty is a major component in driving, there cannot be just one right answer to a prediction for the trajectory or the behaviour, and it becomes important to account for and model that uncertainty. Several approaches have been tried for generating the future scenarios for a vehicle and one such pioneering work set out to model the behaviour of the vehicles probabilistically while tackling the challenges of representation, flexibility, and transferability within one system. The proposed system is called the Semantic Graph Network (SGN) which utilizes feedforward neural networks, Gated Recurrent Units (GRU), and a generative model called the Mixed Density Network to serve its purpose. This thesis project set out in the direction of the implementation of this research work in the context of highway merger scenario and consists of three parts. The first part involves basic data analysis for the employed dataset, whereas the second part involves a model that implements certain parts of the SGN including a variation of the context encoding and the Mixture Density Network. The third and the final part is an attempt to recreate the SGN itself. While the first and the second parts were implemented successfully, for the third part, only certain objectives could be achieved. / Vid autonom körning kan scenariegenerering spela en avgörande roll när det gäller verifieringen av programvaran för autonom körning. Eftersom osäkerhet är en viktig komponent i körning kan det inte bara finnas ett rätt svar på en förutsägelse av banan eller beteendet, och det blir viktigt att redogöra för och modellera den osäkerheten. Flera tillvägagångssätt har prövats för att generera framtidsscenarierna för ett fordon och ett sådant banbrytande arbete gick ut på att modellera fordonens beteende sannolikt samtidigt som utmaningarna med representation, flexibilitet och överförbarhet inom ett system hanteras. Det föreslagna systemet kallas Semantic Graph Network (SGN) som använder neurala nätverk, Gated Recurrent Units (GRU) och en generativ modell som kallas Mixed Density Network för att tjäna sitt syfte. Detta examensarbete riktar sig mot genomförandet av detta forskningsarbete i samband med motorvägssammanslagningsscenariot och består av tre delar. Den första delen involverar grundläggande dataanalys för den använda datamängden, medan den andra delen involverar en modell som implementerar vissa delar av SGN inklusive en variation av kontextkodningen och Mixture Density Network. Den tredje och sista delen är ett försök att återskapa själva SGN. Även om den första och den andra delen genomfördes framgångsrikt, kunde endast vissa mål uppnås för den tredje delen.