On the Prospects of Using Machine Learning for the Numerical Simulation of PDEs: Training Neural Networks to Assemble Approximate Inverses

In an unconventional approach to combining the very successful Finite Element Methods (FEM) for PDE-based simulation with techniques evolved from the domain of Machine Learning (ML) we employ approximate inverses of the system matrices generated by neural networks in the linear solver. We demonstrate the success of this solver technique on the basis of the Poisson equation which can be seen as a fundamental PDE for many practically relevant simulations [Turek 1999]. We use a basic Richardson iteration applying the approximate inverses generated by fully connected feedforward multilayer perceptrons as preconditioners

A Simulation Suite for Lattice-Boltzmann based Real-Time CFD Applications Exploiting Multi-Level Parallelism on Modern Multi- and Many-Core Architectures

We present a software approach to hardware-oriented numerics which builds upon an augmented, previously published open-source set of libraries facilitating portable code development and optimisation on a wide range of modern computer architectures. In order to maximise eficiency, we exploit all levels of arallelism, including vectorisation within CPU cores, the Cell BE and GPUs, shared memory thread-level parallelism between cores, and parallelism between heterogeneous distributed memory resources in clusters. To evaluate and validate our approach, we implement a collection of modular building blocks for the easy and fast assembly and development of CFD applications based on the shallow water equations: We combine the Lattice-Boltzmann method with i-uid-structure interaction techniques in order to achieve real-time simulations targeting interactive virtual environments. Our results demonstrate that recent multi-core CPUs outperform the Cell BE, while GPUs are significantly faster than conventional multi-threaded SSE code. In addition, we verify good scalability properties of our application on small clusters

A Simulation Suite for Lattice-Boltzmann based Real-Time CFD Applications Exploiting Multi-Level Parallelism on Modern Multi- and Many-Core Architectures

We present a software approach to hardware-oriented numerics which builds upon an augmented, previously published open-source set of libraries facilitating portable code development and optimisation on a wide range of modern computer architectures. In order to maximise eficiency, we exploit all levels of arallelism, including vectorisation within CPU cores, the Cell BE and GPUs, shared memory thread-level parallelism between cores, and parallelism between heterogeneous distributed memory resources in clusters. To evaluate and validate our approach, we implement a collection of modular building blocks for the easy and fast assembly and development of CFD applications based on the shallow water equations: We combine the Lattice-Boltzmann method with i-uid-structure interaction techniques in order to achieve real-time simulations targeting interactive virtual environments. Our results demonstrate that recent multi-core CPUs outperform the Cell BE, while GPUs are significantly faster than conventional multi-threaded SSE code. In addition, we verify good scalability properties of our application on small clusters

HONEI: A collection of libraries for numerical computations targeting multiple processor architectures.

We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI's libraries, we achieve a two-fold speedup over straight forward C++ code using HONEI's SSE backend, and additional 3--4 and 4--16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development

The ICARUS white paper. A scalable energy-efficient, solar-powered HPC center based on low power GPUs

We present a unique approach for integrating research in High Performance Computing (HPC) as well as photovoltaic (PV) solar farming and battery technologies into a container-based compute center designed for a maximum of energy efficiency, performance and extensibility/scalability. We use NVIDIA Jetson TK1 boards to build a considerably dimensioned cluster of 60 low-power GPUs, attach a 7:5 kWp solar farm and a 8 kWh Lithium-Ion battery power supply and integrate everything into a single-container, standalone housing. We demonstrate the success of our system by evaluating the performance and energy efficiency for common versatile dense and sparse linear algebra kernels as well as a full CFD code. By this work we can show, that with current technology, energy consumption-induced follow-up cost of HPC can be reduced to zero

Basic Machine Learning Approaches for the Acceleration of PDE Simulations and Realization in the FEAT3 Software

In this paper we present a holistic software approach based on the FEAT3 software for solving multidimensional PDEs with the Finite Element Method that is built for a maximum of performance, scalability, maintainability and extensibilty. We introduce basic paradigms how modern computational hardware architectures such as GPUs are exploited in a numerically scalable fashion. We show, how the framework is extended to make even the most recent advances on the hardware market accessible to the framework, exemplified by the ubiquitous trend to customize chips for Machine Learning. We can demonstrate that for a numerically challenging model problem, artificial neural networks can be used while preserving a classical simulation solution pipeline through the incorporation of a neural network preconditioner in the linear solve