DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).Comment: LDAV 2018, October 201

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

acceptedVersio

High performance simulations of yield stress fluids in a structured adaptive mesh refinement framework with embedded boundaries

Viscoplastic fluids are a class of non-Newtonian liquids characterised by their yield stress. Unless an external stress is applied which is larger than this threshold value, the fluid does not flow, but exhibits rigid body behaviour. Above the yield stress, applied forces cause viscous deformation. Such fluids play important roles in a range of fields, notably in wellbore drilling, which is the application that motivated this project. One aspect of this operation requires displacement of drilling fluid by cement in the annulus between casing and geological surroundings, and both of these fluids are viscoplastics. Ensuring that this is done properly is of utmost importance to the overall safety of the drilling operation. Often, numerical simulations are the only viable way of experimenting with the effect of drilling parameters and fluid properties on the flow configuration and resulting behaviour. Unfortunately, the presence of a yield stress leads to a singularity in the apparent viscosity at zero strain. This causes substantial computational expense for the algorithms used to simulate fluid flow numerically, even when regularisation techniques are employed to alleviate the problem. Consequently, most published results in the literature on computational viscoplasticity has been restricted to two-dimensional and steady-state flows. In an attempt to address this, we have applied state-of-the-art techniques from high-performance computational fluid dynamics to the viscoplastic flow problem. Specifically, we utilise spatio-temporal adaptive mesh refinement on structured meshes in this context for the first time. This is achieved through the software framework AMReX, which includes state-of-the-art numerical tools for solving partial differential equations with optimal parallel scaling. The ability to rapidly simulate unsteady viscoplastic flow problems in three dimensions is demonstrated by novel numerical experiments in a lid-driven cavity. In order to investigate flows in more interesting domain geometries and around objects, an embedded boundary algorithm has been developed which works alongside the viscoplastic flow solver. We show how this methodology can be utilised to simulate flow inside non-rectangular objects, and investigate fully three-dimensional viscoplastic flow past several shapes of bodies for the first time.EPSRC Centre for Doctoral Training in Computational Methods for Materials Science grant number EP/L015552/1 BP International Centre for Advanced Materials (BP-ICAM) Extra support towards living expenses through the Aker Scholarshi

Synergies between Numerical Methods for Kinetic Equations and Neural Networks

The overarching theme of this work is the efficient computation of large-scale systems. Here we deal with two types of mathematical challenges, which are quite different at first glance but offer similar opportunities and challenges upon closer examination. Physical descriptions of phenomena and their mathematical modeling are performed on diverse scales, ranging from nano-scale interactions of single atoms to the macroscopic dynamics of the earth\u27s atmosphere. We consider such systems of interacting particles and explore methods to simulate them efficiently and accurately, with a focus on the kinetic and macroscopic description of interacting particle systems. Macroscopic governing equations describe the time evolution of a system in time and space, whereas the more fine-grained kinetic description additionally takes the particle velocity into account. The study of discretizing kinetic equations that depend on space, time, and velocity variables is a challenge due to the need to preserve physical solution bounds, e.g. positivity, avoiding spurious artifacts and computational efficiency. In the pursuit of overcoming the challenge of computability in both kinetic and multi-scale modeling, a wide variety of approximative methods have been established in the realm of reduced order and surrogate modeling, and model compression. For kinetic models, this may manifest in hybrid numerical solvers, that switch between macroscopic and mesoscopic simulation, asymptotic preserving schemes, that bridge the gap between both physical resolution levels, or surrogate models that operate on a kinetic level but replace computationally heavy operations of the simulation by fast approximations. Thus, for the simulation of kinetic and multi-scale systems with a high spatial resolution and long temporal horizon, the quote by Paul Dirac is as relevant as it was almost a century ago. The first goal of the dissertation is therefore the development of acceleration strategies for kinetic discretization methods, that preserve the structure of their governing equations. Particularly, we investigate the use of convex neural networks, to accelerate the minimal entropy closure method. Further, we develop a neural network-based hybrid solver for multi-scale systems, where kinetic and macroscopic methods are chosen based on local flow conditions. Furthermore, we deal with the compression and efficient computation of neural networks. In the meantime, neural networks are successfully used in different forms in countless scientific works and technical systems, with well-known applications in image recognition, and computer-aided language translation, but also as surrogate models for numerical mathematics. Although the first neural networks were already presented in the 1950s, the scientific discipline has enjoyed increasing popularity mainly during the last 15 years, since only now sufficient computing capacity is available. Remarkably, the increasing availability of computing resources is accompanied by a hunger for larger models, fueled by the common conception of machine learning practitioners and researchers that more trainable parameters equal higher performance and better generalization capabilities. The increase in model size exceeds the growth of available computing resources by orders of magnitude. Since $2012$, the computational resources used in the largest neural network models doubled every $3.4$ months\footnote{\url{https://openai.com/blog/ai-and-compute/}}, opposed to Moore\u27s Law that proposes a $2$-year doubling period in available computing power. To some extent, Dirac\u27s statement also applies to the recent computational challenges in the machine-learning community. The desire to evaluate and train on resource-limited devices sparked interest in model compression, where neural networks are sparsified or factorized, typically after training. The second goal of this dissertation is thus a low-rank method, originating from numerical methods for kinetic equations, to compress neural networks already during training by low-rank factorization. This dissertation thus considers synergies between kinetic models, neural networks, and numerical methods in both disciplines to develop time-, memory- and energy-efficient computational methods for both research areas

Numerical Particle-In-Cell studies of Hall thrusters using unstructured grids

In a few decades, space has become a crucial part of our modern society. With the imminent deployment of mega satellite constellations, their number will increase dramatically. These future satellites will be mainly equipped with electric propulsion systems, and in particular Hall thrusters. However, the processes governing the plasma physics within Hall thrusters remain poorly understood, which forces manufacturers to carry out costly and laborious experimental campaigns to certify the finished product. To overcome this difficulty, numerical simulations are essential. They can be based on a Particle-In-Cell (PIC) method, well adapted to the physics of this type of plasma. Indeed, these plasmas present kinetic effects that cannot be accurately described by fluid methods. Due to the cost of PIC simulations and the complex phenomena involved, existing codes in the literature remain limited to academic configurations based on structured meshes. In an effort to overcome these challenges, the AVIP PIC code is developed at CERFACS as a predictive tool capable of modeling industrial configurations. To do this, AVIP PIC works with unstructured meshes, which no other code in the community can currently do. This innovation comes at the cost of a considerable complexity of the code and a substantial optimization work was first done in previous work. Because of its innovative character, the first objective of this thesis was to systematically validate AVIP PIC. Thus, AVIP PIC was first used to participate successfully in an international benchmark on a 2D configuration in the axial-azimuthal plane. During this work, all groups obtained close results with 5% difference at most on the main plasma parameters profiles. An azimuthal plasma oscillation, the electron drift instability, was also observed by all participants with extremely similar characteristics. This instability due to kinetic effects, most probably plays a fundamental role in the anomalous transport of electrons within the engine. Based on this first success, we then used this case to explore and parameterize an active particle control algorithm. By preventing the number of particles from increasing too much, this tool reduces the computational cost and will be very useful in future simulations. Still, in the perspective of code validation, we then studied a simplified 2D configuration in the radial- azimuthal plane of the engine. Indeed, taking into account the presence of the walls can considerably modify the simulated physics of the engine. In particular, we have highlighted a radial-azimuthal instability, also called modified two-stream instability, which is coupled to the electron drift instability mentioned above. A benchmark work, conducted by CERFACS with six international groups, confirmed this result with an excellent agreement, despite the great diversity of the codes involved. Capitalizing on our experience in 2D, we then developed a 3D simulation based on the same geometrical elements and plasma conditions than in the two previous cases. During this study the 3D electron drift instability was identified as well as a possible signature of the radial- azimuth instability. The comparison with the previous 2D configurations seems to show that the 2D simulations tend to create a hotter and denser plasma, which affects the oscillatory phenomena. The general structure of the plasma remains nevertheless similar. Finally tools for the analysis of the code performance have been developed which will prove to be valuable for the development of more advanced 3D configurations