اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBenefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
297
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.
قيم البحث
اقرأ أيضاً
We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precisi
on floating point operations on Nvidias A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent fractional occupation numbers of the electronic states at finite temperatures.
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse lin
ear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented.
An implementation of a lattice-based approach for computing the topological skyrmion charge is provided for the open source micromagnetics code MuMax3. Its accuracy with respect to an existing method based on finite difference derivatives is compared
for three different test cases. The lattice-based approach is found to be more robust for finite-temperature dynamics and for nucleation and annihilation processes in extended systems.
The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechan
ical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver (VQE) algorithm. To this end, we consider three isoelectronic species, namely Be, Li-, and B+. This unique choice spans three classes, a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster (UCC) ansatz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the UCC methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a VQE algorithm is repeated to build statistics) required for calculations with IBM Qiskits QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the VQE algorithm.
We explore the application of computer vision and machine learning (ML) techniques to predict material properties (e.g. compressive strength) based on SEM images. We show that its possible to train ML models to predict materials performance based on
SEM images alone, demonstrating this capability on the real-world problem of predicting uniaxially compressed peak stress of consolidated molecular solids samples. Our image-based ML approach reduces mean absolute percent error (MAPE) by an average of 24% over baselines representative of the current state-of-the-practice (i.e., domain-experts analysis and correlation). We compared two complementary approaches to this problem: (1) a traditional ML approach, random forest (RF), using state-of-the-art computer vision features and (2) an end-to-end deep learning (DL) approach, where features are learned automatically from raw images. We demonstrate the complementarity of these approaches, showing that RF performs best in the small data regime in which many real-world scientific applications reside (up to 24% lower RMSE than DL), whereas DL outpaces RF in the big data regime, where abundant training samples are available (up to 24% lower RMSE than RF). Finally, we demonstrate that models trained using machine learning techniques are capable of discovering and utilizing informative crystal attributes previously underutilized by domain experts.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
