High-performance Numerical Computing Research Articles

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10× acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research. Program summaryProgram Title: JAX-FEMCPC Library link to program files:https://doi.org/10.17632/hgwshjbcw6.1Developer's repository link:https://github.com/tianjuxue/jax-am/tree/main/jax_am/femLicensing provisions: GPLv3Programming language: PythonNature of problem: Implementation of the finite element method (FEM) with several appealing features that classic FEM software typically does not have: realized with pure Python; running on CPU/GPU; differentiable for solving PDE-constrained optimization problems; seamless integration with machine learning.Solution method: Our framework JAX-FEM is based on Google JAX, a high-performance numerical computing library with automatic differentiation features and supporting both CPU/GPU. Unlike classic FEM software written in Fortran or C/C++, JAX-FEM is implemented with pure Python and can easily be installed as a Python package. We demonstrate our software by solving problems including forward PDE prediction, inverse design/optimization, and data-driven analysis.

Optimal control of the treatment and the vaccination in an epidemic switched system using polynomial approach

We study the problem of optimal switching on a treatment-vaccination model with four switches. These switches provide a more realistic approach when dealing with the control of an epidemic. We have used a relatively new approach to investigate optimal switching. The main idea behind this approach is to convert the switched system, a nonlinear, nonconvex optimal control problem, into an equivalent optimal control problem with a linear and convex structure. This allows us to obtain an equivalent convex formulation better suited to being solved by high-performance numerical computing. Toward the end, we perform some numerical simulations and draw the conclusion that the presence of treatment is essential, whereas vaccination control can be used at intervals with progressively larger gaps between the intervals.

Development of MATLAB Codes to Find the Natural Frequencies of a Composite Structure

Modal analysis is a method to describe the dynamic properties of structure such as natural frequency, mode shape and damping ratio. These properties are important for design and analysis of structure in dynamic condition. MATLAB is a high-performance numerical computation and visualization software package. It provides an interactive environment with hundreds of built-in functions for technical computation, graphics, and animation. In present analysis, use of MATLAB is done for finding the free vibrational characteristics of a structure made of composite material. The study involves finding the natural frequencies of structure made of Glass-epoxy, Carbon-epoxy and Graphite fiber reinforced polyamide materials. In this case Euler’s-Bernoulli beam theory is used for analytical solution and to construct MATLAB codes. The structure considered here is a beam with fixed-free condition. The results obtained from the MATLAB are accurate comparatively, the results obtained shows that the MATLAB can be further used to write programs which involve complicated iterations and cannot be done manually. The further work can be extended for writing the programs of much more complex equations in MATLAB and obtains exact solution.

A Framework for Remote Sensing Images Processing Using Deep Learning Techniques

Deep learning techniques are becoming increasingly important to solve a number of image processing tasks. Among common algorithms, Convolutional Neural Networks and Recurrent Neural Networks based systems achieve state of the art results on satellite and aerial imagery in many applications. While these approaches are subject to scientific interest, there is currently no operational and generic implementation available at user-level for the remote sensing community. In this paper, we presents a framework enabling the use of deep learning techniques with remote sensing images and geospatial data. Our solution takes roots in two extensively used open-source libraries, the remote sensing image processing library Orfeo ToolBox, and the high performance numerical computation library TensorFlow. It can apply deep nets without restriction on images size and is computationally efficient, regardless hardware configuration.

DEVELOPING GRAPHICAL USER INTERFACE FOR ANALYSIS OF BEAM BY USING MATLAB SOFTWARE

Since Beam is an important member of any structure and carries heavy loads and hence before using beams one should have to be very sure about its shear strength and bending strength. Industrial beams have different types of support and structural properties. Various types of loads are acting on it like point loads, distributed loads etc. Shear stresses and bending moment should be within the material allowable limits and therefore analysis of beam is essential. In present work the analysis of beam is carried out by using GRAPHICAL USER INTERFACE (GUI) developed in software called MATLAB. This gives the package for high-performance numerical computation and visualization.

Optimal Control of Switching Topology Networks

We present an extension of a previously proposed approach based on the method of moments for solving the optimal control problem for a switching system considering now a continuous external input. This method is based on the transformation of a nonlinear, nonconvex optimal control problem, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high-performance numerical computing. Finally, the design of optimal logic-based controllers for networked systems with a dynamic topology is presented as an application of this work.

High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

Modern physics is based on both theoretical analysis and experimental validation. Complex scenarios like subatomic dimensions, high energy, and lower absolute temperature are frontiers for many theoretical models. Simulation with stable numerical methods represents an excellent instrument for high accuracy analysis, experimental validation, and visualization. High performance computing support offers possibility to make simulations at large scale, in parallel, but the volume of data generated by these experiments creates a new challenge for Big Data Science. This paper presents existing computational methods for high energy physics (HEP) analyzed from two perspectives: numerical methods and high performance computing. The computational methods presented are Monte Carlo methods and simulations of HEP processes, Markovian Monte Carlo, unfolding methods in particle physics, kernel estimation in HEP, and Random Matrix Theory used in analysis of particles spectrum. All of these methods produce data-intensive applications, which introduce new challenges and requirements for ICT systems architecture, programming paradigms, and storage capabilities.

A polynomial approach for optimal control of switched nonlinear systems

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high-performance numerical computing. Consequently, we propose to convexify the control variables by means of the method of moments obtaining semidefinite programs. Copyright © 2013 John Wiley & Sons, Ltd.

Parameter Transfer Method of Mixed-Language Programming

The mixed-language programming is using two kinds of programming language or more to develop application. During the process of handling many engineering problems, the complex computation is often needed. So the method of mixed-language programming is often used in developing project software. MATLAB is high-performance numerical computation software, and VC++ is a considerably mature application development platform. They are often use in mix programming. During the process of VC++ and MATLAB mixed-language programming, when it calls algorithm function written in MATLAB in the VC++ environment, sometimes the parameters could not be easily passed to objective function. In this paper, a method resolving the parameters transfer of objective function is proposed. That is in the declaration of algorithm function canceling the objective function as one of its parameters, and adding the parameters of the objective function to the parameter of the algorithm function. Finally, a case of parallelism error evaluation system is given to illustrate feasibility of proposed method.

JaceP2P, une infrastructure pair-à-pair basée sur le calcul itératif asynchrone

Peer-To-Peer (P2P) systems represent a decentralized alternative to classical clientserver architectures. In particular, they allow to use a vast amount of distributed resources connected to internet in order to perform high performance numerical computation in a parallel way on decentralized architectures. The aim of our work is to execute scientific iterative applications on a P2P network. We present the JaceP2P platform, a Peer-To-Peer library suited to design and execute asynchronous iterative algorithms. JaceP2P is a Java multithreaded environment which allows to develop scientific iterative applications in order to execute them on a P2P network of heterogeneous and dynamic machines.

A Unified Framework for Numerical and Combinatorial Computing

A rich variety of tools help researchers with high-performance numerical computing, but few tools exist for large-scale combinatorial computing. The authors describe their efforts to build a common infrastructure for numerical and combinatorial computing by using parallel sparse matrices to implement parallel graph algorithms.

High-performance computing of for a vector of inputs on Alpha and IA-64 CPUs

The modern microprocessors have become more sophisticated, the performance of software on modern architectures has grown more and more difficult to dissect and prognosticate. The execution of a program nowadays entails the complex interaction of code, compiler and processor micro-architecture. The built-in functions to compute 1/x or exp(+/-x) of math library and hardware are often incapable of achieving the challenging performance of high-performance numerical computing. To meet this demand, the current trend in constructing high-performance numerical computing for specific processors Alpha 21264 & 21364, and IA-64 has been optimized for 1/xi and exp(+/-xi) for a vector of inputs xi which is significantly faster than optimized library routines. A detailed deliberation of how the processor micro-architecture as well as the manual optimization techniques improve the computing performance has been developed.

Floating-Point Speculation for High-Performance Numerical Computing in Java

Floating-Point Speculation for High-Performance Numerical Computing in Java

Java programming for high-performance numerical computing

First proposed as a mechanism for enhancing Web content, the Java™ language has taken off as a serious general-purpose programming language. Industry and academia alike have expressed great interest in using the Java language as a programming language for scientific and engineering computations. Applications in these domains are characterized by intensive numerical computing and often have very high performance requirements. In this paper we discuss programming techniques that lead to Java numerical codes with performance comparable to FORTRAN or C, the more traditional languages for this field. The techniques are centered around the use of a high-performance numerical library, written entirely in the Java language, and on compiler technology. The numerical library takes the form of the Array package for Java. Proper use of this package, and of other appropriate tools for compiling and running a Java application, results in code that is clean, portable, and fast. We illustrate the programming and performance issues through case studies in data mining and electromagnetism.

The mu VP 64-bit vector coprocessor: a new implementation of high-performance numerical computation

The architecture and design of the mu VP, a single-chip vector coprocessor developed to meet the needs of high-performance processors, are described. The mu VP is a supercomputer component implemented on a single large-scale-integrated (LSI) CMOS chip. With 206 MFLOPS single-precision and 106-MFLOPS double-precision performance at 50 MHz, the mu VP offers a rate almost equivalent to that typical minisupercomputers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new software architecture for parallel computation and visualization

A novel mathematical data model is investigated as a basis for software environments integrating high performance numerical computation, spontaneous visualization, computation steering, and visual programming in the context of distributed, parallel or network computing. By implementing this data model using enhanced versions of several existing software technologies, we plan to create an entirely new sort of computational environment that will make it much easier for scientists to focus the coming generation of high performance, parallel computers on compute-intensive scientific problems.