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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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94 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high-resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as a MPS within some tolerable error threshold. Here, in this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations for systems with one coordinate in space and one coordinate in velocity, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher-dimensional problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Performance of the rigorous renormalization group for first-order phase transitions and topological phases

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in one-dimensional systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau [Nat. Phys. 11, 566 (2015)1745-247310.1038/nphys3345]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first-order phase transitions and in symmetry-protected topological phases. Our study is motivated by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first-order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near-)degenerate manifolds. Furthermore, the rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines well-ordered, accurate energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Automatic Generation of High-Performance Convolution Kernels on ARM CPUs for Deep Learning

In this work, we present FastConv, a template-based code auto-generation open source library that can automatically generate high-performance deep learning convolution kernels of arbitrary matrices/tensors shapes. FastConv is based on the Winograd algorithm, which is reportedly the highest performing algorithm for the time-consuming convolution layers of convolutional neural networks. ARM CPUs cover a wide range designs and specifications, from embedded devices to HPC-grade CPUs. The leads to the dilemma of how to consistently optimize Winograd-based convolution solvers for convolution layers of different shapes. FastConv addresses this problem by using templates to auto-generate multiple shapes of tuned kernels variants suitable for skinny tall matrices. As a performance portable library, FastConv transparently searches for the best combination of kernel shapes, cache tiles, scheduling of loop orders, packing strategies, access patterns, and online/offline computations. Auto-tuning is used to search the parameter configuration space for the best performance for a given target architecture and problem size. The experiments with layer-wise evaluation on the VGG--16 model confirms a 1.25x performance gains is got by tuning the Winograd library. Integrated comparison results shows 1.02x to 1.40x, 1.14x to 2.17x, and 1.22x and 2.48x speedup is achieved over NNPACK, Arm NN, and FeatherCNN on the Kunpeng 920 beside few cases. Furthermore, problem size performance portability experiments with various convolution shapes shows that FastConv achieves 1.2x to 1.7x speedup and 2x to 22x speedup over NNPACK and ARM NN inference engine using Winograd on Kunpeng 920 . CPU performance portability evaluation on the VGG--16 show an average speedup over NNPACK of 1.42x, 1.21x, 1.26x, 1.37x, 2.26x, and 11.02x is observed on Kunpeng 920, Snapdragon 835, 855, 888, Apple M1, and AWS Graviton2, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed “𝔤-sim”, which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exist observables for which the simulation is efficient. Indeed, we show that 𝔤-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and nonvariational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of 𝔤-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, nonequivalent resources for classical simulation.

97 MATHEMATICS AND COMPUTING↗