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.

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<p></p><p></p><p>Peatlands are the most efficient natural carbon sink on the planet. They are the most carbon-intensive storages than any other vegetation types. However, recent studies indicate that global peatlands can potentially release 6% of the global soil carbon into the atmosphere when they are drained or deforested. They cover only about 3% of the total global land area, but sequester over 30% of the Earth’s soil organic carbon. Peatlands in northern mid-to-high latitudes (45°-90°N) occupy ~90% of the global peatland area and account for ~80% of the total global peat organic carbon stock. Those peatlands are mainly located in Canada, Russia, and the USA. Peatlands in tropical regions cover ~10% of the global peatlands area and store 15-19% of the global peat organic carbon. They are mainly distributed in Southeast Asia and South and Central America. The temperature at the global scale has been rising since the middle of the last century and has accelerated during the last 40 years and the warming will continue in this century. The large storage of soil organic carbon within the peatlands can significantly respond to the changing climate by varying the roles between their carbon sink (from atmosphere to soil) and source (from soil to atmosphere) activities. This dissertation focuses on quantifying the soil organic carbon dynamics in North America and South America using mechanistically-based biogeochemistry models. </p><p></p><p>Peatlands in Alaska occupy 40 million hectares and account for ~10% of the total peatland area in northern mid-to-high latitudes. The regional soil organic carbon dynamics and its response to climate are still with large uncertainty. Most of the studies on peatlands to date are based on short-term site-level observation. This dissertation first used an integrated modeling framework that coupled the dynamics of hydrology, soil thermal regime, and ecosystem carbon and nitrogen to quantify the long-term peat carbon accumulation in Alaska during the Holocene. Modeled hydrology, soil thermal regime, carbon pools and fluxes and methane emissions were evaluated using long-term observation data at several peatland sites in Minnesota, Alaska, and Canada. The model was then applied for a 10,000-year (15 ka to 5 ka; 1 ka = 1000 cal yr before present) simulation at four peatland sites. The model simulations matched the observed carbon accumulation rates at fen sites during the Holocene (R^2= 0.88, 0.87, 0.38 and -0.05 for four sites respectively using comparisons in 500-year bins from 15 ka to 5 ka). The simulated (2.04 m) and observed peat depths (on average 1.98 m) also compared well (R^2 = 0.91). The early Holocene carbon accumulation rates, especially during the Holocene thermal maximum (HTM) (35.9 g 〖C m〗^(-2) yr^(-1)), were estimated up to 6-times higher than the rest of the Holocene (6.5 g 〖C m〗^(-2) yr^(-1)). It suggested that high summer temperature and the lengthened growing season resulted from the elevated insolation seasonality, along with wetter-than-before conditions might be major factors causing the rapid carbon accumulation in Alaska during the HTM. The sensitivity tests indicated that, apart from climate, initial water-table depth and vegetation canopy were major drivers to the estimated peat carbon accumulation. </p><p></p><p>To further quantify the regional long-term soil organic carbon accumulation rates and the current carbon stocks in Alaska, the second part of my research focused on quantifying the soil organic carbon accumulation in multiple Alaskan terrestrial ecosystems over the last 15,000 years for both peatland and non-peatland ecosystems. Comparable with the previous estimates of 25-70 Pg carbon (C) in peatlands and 13-22 Pg C in non-peatland soils within 1-m depth in Alaska using peat core data, our model estimated a total SOC of 36-63 Pg C at present, including 27-48 Pg C in peatland soils and 9-15 Pg C in non-peatland soils. Current living vegetation stored 2.5-3.7 Pg C in Alaska with 0.3-0.6 Pg C in peatlands and 2.2-3.1 Pg C in non-peatlands. The simulated average rate of peat soil C accumulation was 2.3 Tg C yr^(-1) with a peak value of 5.1 Tg C yr^(-1) during the Holocene Thermal Maximum (HTM) in the early Holocene, four folds higher than the average rate of 1.4 Tg C yr^(-1) over the rest of the Holocene. The accumulation slowed down, or even ceased, during the neo-glacial climate cooling after the mid-Holocene, but increased again in the 20th century. The model-estimated peat depths ranged from 1.1 to 2.7 m, similar to the field-based estimate of 2.29 m for the region. The changes in vegetation and their distributions were the main factors to determine the spatial variations of SOC accumulation during different time periods. Warmer summer temperature and stronger radiation seasonality, along with higher precipitation in the HTM and the 20th century might have resulted in the extensive peatland expansion and carbon accumulation. </p><p>Most studies on the role of tropical peatlands have focused on Indonesian peatlands. Few have focused on the Amazon basin, where peatlands remain intact and have been a long-term carbon sink. To address the problem, my third study quantified the carbon accumulation for peatland and non-peatland ecosystems in the Pastaza-Marañon foreland basin (PMFB), the most extensive peatland complex in the Amazon basin from 12,000 years before present to 2100 AD. Model simulations indicated that warming accelerated peat carbon loss while increasing precipitation accelerated peat carbon accumulation at millennial time scales. The uncertain parameters and spatial variation of climate were significant sources of uncertainty to modeled peat carbon accumulation. Under warmer and presumably wetter conditions over the 21st century, the warming effect on increasing peat carbon loss might overwhelm the wetter effect on increasing peat carbon accumulation. Peat soil carbon accumulation rate in the PMFB slowed down to 7.9 (4.3~12.2) g C m^(-2) yr^(-1) from the current rate of 16.1 (9.1~23.7) g C m^(-2) yr^(-1) and the region might turn into a carbon source to the atmosphere at -53.3 (-66.8~-41.2) g C m^(-2) yr^(-1) (negative indicates source), depending on the level of warming. Peatland ecosystems showed a higher vulnerability than non-peatland ecosystems as indicated by the ratio of their soil carbon density changes (change of soil carbon/existing soil carbon stock) ranging from 3.9 to 5.8). This was primarily due to larger peatlands carbon stocks and more dramatic responses of their aerobic and anaerobic decompositions in comparison with non-peatland ecosystems under future climate conditions. Peatland and non-peatland soils in the PMFB might lose up to 0.4 (0.32~0.52) Pg C by 2100 AD with the largest loss from palm swamp. The carbon-dense Amazonian peatland might switch from a current carbon sink into a source in the 21st century.</p><p>Peatlands are important sources and sinks for greenhouse gases (carbon dioxide and methane). Their carbon (C) balance between soil and atmosphere remains unquantified due to the large data gaps and uncertainties in regional peat carbon estimation. My final study was to quantify the C accumulation rates and C stocks within North America peatlands over the last 12,000 years. I find that 85-174 Pg C have been accumulated in North American peatlands over these years including 0.37-0.76 Pg C in subtropical peatlands in this region. During the 10- 8 ka period, the warmer and wetter conditions might have played an important role in stimulating peat C accumulation by enhancing plant photosynthesis. The enhanced peat decomposition due to warming through the Holocene slows down carbon accumulation in the region.</p><div><br></div><p><br></p>

The goal of this thesis is to synthesize believable motions of a character interacting with its surroundings and manipulating objects through physical contacts and forces. Human-like autonomous avatars are in increasing demand in areas such as entertainment, education, and health care. Yet modeling the basic human motor skills of locomotion and manipulation remains a long-standing challenge in animation research. The seemingly simple tasks of navigating an uneven terrain or grasping cups of different shapes involve planning with complex kinematic and physical constraints as well as adaptation to unexpected perturbations. Moreover, natural movements exhibit unique personal characteristics that are complex to model. Although motion capture technologies allow virtual actors to use recorded human motions in many applications, the recorded motions are not directly applicable to tasks involving interactions for two reasons. First, the acquired data cannot be easily adapted to new environments or different tasks goals. Second, acquisition of accurate data is still a challenge for fine scale object manipulations. In this work, we utilize data to create natural looking animations, and mitigate data deficiency with physics-based simulations and numerical optimizations. We develop algorithms based on a single reference motion for three types of control problems. The first problem focuses on motions without contact constraints. We use joint torque patterns identified from the captured motion to simulate responses and recovery of the same style under unexpected pushes. The second problem focuses on locomotion with foot contacts. We use contact forces to control an abstract dynamic model of the center of mass, which sufficiently describes the locomotion task in the input motion. Simulation of the abstract model under unexpected pushes or anticipated changes of the environment results in responses consistent with both the laws of physics and the style of the input. The third problem focuses on fine scale object manipulation tasks, in which accurate finger motions and contact information are not available. We propose a sampling method to discover contact relations between the hand and the object from only the gross motion of the wrists and the object. We then use the abundant contact constraints to synthesize detailed finger motions. The algorithm creates finger motions of various styles for a diverse set of object shapes and tasks, including ones that are not present at capture time. The three algorithms together control an autonomous character with dexterous hands to interact naturally with a virtual world. Our methods are general and robust across character structures and motion contents when testing on a wide variety of motion capture sequences and environments. The work in this thesis brings closer the motor skills of a virtual character to its human counterpart. It provides computational tools for the analysis of human biomechanics, and can potentially inspire the design of novel control algorithms for humanoid robots.

L’utilisation de personnages virtuels dans le cadre de simulations basées sur les lois de la physique trouve maintenant des applications allant de la biomécanique à l’animation. L’un des éléments incontournables de cette performance est le contrôleur de mouvement, capable de transformer les actions souhaitées en mouvements synthétisés. La conceptualisation de ces contrôleurs a profondément évolué grâce à l'apport des connaissances en biomécanique qui a conduit à l'utilisation de modèles de personnages encore plus détaillés car s'inspirant de l’appareil squelettique et surtout musculaire de l’être humain (ou personnages à modèle musculaire). Contrôler les personnages virtuels implique un défi de taille : contrôler la redondance, ou le fait même qu’un nombre important de muscles ou d’actionneurs aient besoin d’être contrôlés simultanément pour exécuter la tâche de motricité demandée.L’objectif de cette thèse est d’y répondre en s’inspirant du système de contrôle moteur humain permettant de gérer cette redondance. Une solution de contrôle, pour les personnages virtuels, est proposée d’après la théorie des synergies musculaires et appliquée à des mouvements de contrôle du lancer. Les synergies musculaires sont des représentations de contrôle à faible dimension et qui permettent aux muscles d’être contrôlés en groupe, réduisant ainsi de manière significative le nombre de variables. Grâce à cette stratégie, cette thèse permet les contributions suivantes : en premier lieu, la validation de la théorie des synergies musculaires, utilisée ici pour étudier un nouveau mouvement et pour tenter de contrôler un personnage virtuel. Et elle contribue également à l'ensemble des domaines impliquant des simulations corporelles, ayant recours aux personnages à modèle musculaire (comme par exemple, la biomécanique ou l'animation) en leur proposant une solution de contrôle permettant de réduire la redondance. / The use of virtual characters in physics-based simulations has applications that range from biomechanics to animation. An essential component behind such applications is the character’s motion controller, which transforms desired tasks into synthesized motions. The way these controllers are designed is being profoundly transformed through the integration of knowledge from biomechanics, which motivates the idea of using more detailed character models, inspired by the human musculoskeletal system (or muscle-based characters). Controlling these characters implies solving an important challenge: control redundancy, or the fact that numerous muscles or actuators need to be coordinated simultaneously to achieve the desired motion task.The goal of this thesis is to address this challenge by taking inspiration from how the human motor control system manages this redundancy. A control solution for virtual characters is proposed based on the theory of muscle synergies, and applied on the control of throwing motions. Muscle synergies are low-dimensional control representations that allow muscles to be controlled in groups, thus reducing significantly the number of control variables.Through this solution this thesis has the following contributions: 1) A contribution to the validation of the muscle synergy theory by using it to study a new motion, and challenging it with the control of a virtual character, and 2) a contribution to the variety of domains involving physical simulation with muscle-based characters (e.g, biomechanics, animation) by proposing a control solution that reduces redundancy.

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La quête de performance a été une constante à travers l'histoire des systèmes informatiques.Il y a plus d'une décennie maintenant, le modèle de traitement séquentiel montrait ses premiers signes d'épuisement pour satisfaire les exigences de performance.Les barrières du calcul séquentiel ont poussé à un changement de paradigme et ont établi le traitement parallèle comme standard dans les systèmes informatiques modernes.Avec l'adoption généralisée d'ordinateurs parallèles, de nombreux algorithmes et applications ont été développés pour s'adapter à ces nouvelles architectures.Cependant, dans des applications non conventionnelles, avec des exigences d'interactivité et de temps réel, la parallélisation efficace est encore un défi majeur.L'exigence de performance en temps réel apparaît, par exemple, dans les simulations interactives où le système doit prendre en compte l'entrée de l'utilisateur dans une itération de calcul de la boucle de simulation.Le même type de contrainte apparaît dans les applications d'analyse de données en continu.Par exemple, lorsque des donnes issues de capteurs de trafic ou de messages de réseaux sociaux sont produites en flux continu, le système d'analyse doit être capable de traiter ces données à la volée rapidement sur ce flux tout en conservant un budget de mémoire contrôlé.La caractéristique dynamique des données soulève plusieurs problèmes de performance tel que la décomposition du problème pour le traitement en parallèle et la maintenance de la localité mémoire pour une utilisation efficace du cache.Les optimisations classiques qui reposent sur des modèles pré-calculés ou sur l'indexation statique des données ne conduisent pas aux performances souhaitées.Dans cette thèse, nous abordons les problèmes dépendants de données sur deux applications différentes: la première dans le domaine de la simulation physique interactive et la seconde sur l'analyse des données en continu.Pour le problème de simulation, nous présentons un algorithme GPU parallèle pour calculer les multiples plus courts chemins et des diagrammes de Voronoi sur un graphe en forme de grille.Pour le problème d'analyse de données en continu, nous présentons une structure de données parallélisable, basée sur des Packed Memory Arrays, pour indexer des données dynamiques géo-référencées tout en conservant une bonne localité de mémoire. / The quest for performance has been a constant through the history of computing systems. It has been more than a decade now since the sequential processing model had shown its first signs of exhaustion to keep performance improvements.Walls to the sequential computation pushed a paradigm shift and established the parallel processing as the standard in modern computing systems. With the widespread adoption of parallel computers, many algorithms and applications have been ported to fit these new architectures. However, in unconventional applications, with interactivity and real-time requirements, achieving efficient parallelizations is still a major challenge.Real-time performance requirement shows-up, for instance, in user-interactive simulations where the system must be able to react to the user's input within a computation time-step of the simulation loop. The same kind of constraint appears in streaming data monitoring applications. For instance, when an external source of data, such as traffic sensors or social media posts, provides a continuous flow of information to be consumed by an on-line analysis system. The consumer system has to keep a controlled memory budget and delivery fast processed information about the stream.Common optimizations relying on pre-computed models or static index of data are not possible in these highly dynamic scenarios. The dynamic nature of the data brings up several performance issues originated from the problem decomposition for parallel processing and from the data locality maintenance for efficient cache utilization.In this thesis we address data-dependent problems on two different application: one in physics-based simulation and other on streaming data analysis. To the simulation problem, we present a parallel GPU algorithm for computing multiple shortest paths and Voronoi diagrams on a grid-like graph. To the streaming data analysis problem we present a parallelizable data structure, based on packed memory arrays, for indexing dynamic geo-located data while keeping good memory locality.