A fast, hybrid, power-efficient high-precision solver for large linear systems based on low-precision hardware

Angerer, Christoph; Polig, Raphael; Zegarac, D.; Giefers, Heiner; Hagleitner, Christoph; Bekas, Costas; Curioni, A.

doi:10.1016/j.suscom.2015.10.001

Cited by 9 publications

(10 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However MEMs still have many properties that can be exploited for better and faster emulation, which should not be ignored only due to the early state of the method. These known advantages include the suitability for parallelization and, speedups and energy saving via approximated computing [Angerer et al, 2015] 10 3 ) 20.2, 6.9 3.42, 2.8 Table 3: Mean emulation errors corresponding to the Adliswil catchment dataset. MEM refers to an emulator in Machac et al [2016a], while MEM-fit to an emulator with the same proxy structure but parameters fitted to the data.…”

Section: Discussionmentioning

confidence: 99%

“…The iteration in iv) avoids the ill-conditioned covariance matrices [Hansen, 1998] involved in GP when sampling rates are high [Steinke andSchölkopf, 2008, Reichert et al, 2011] and it is faster than direct matrix inversion in a serial implementation. The GP approach i) is better suited for parallelization, speedups and energy saving via approximated computing [Angerer et al, 2015].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models

Carbajal

Leito

Albert

et al. 2017

Environmental Modelling & Software

View full text Add to dashboard Cite

Many model based scientific and engineering methodologies, such as system identification, sensitivity analysis, optimization and control, require a large number of model evaluations. In particular, model based real-time control of urban water infrastructures and online flood alarm systems require fast prediction of the network response at different actuation and/or parameter values. General purpose urban drainage simulators are too slow for this application. Fast surrogate models, so-called emulators, provide a solution to this efficiency demand. Emulators are attractive, because they sacrifice unneeded accuracy in favor of speed. However, they have to be fine-tuned to predict the system behavior satisfactorily. Also, some emulators fail to extrapolate the system behavior beyond the training set. Although, there are many strategies for developing emulators, up until now the selection of the emulation strategy remains subjective. In this paper, we therefore compare the performance of two families of emulators for open channel flows in the context of urban drainage simulators. We compare emulators that explicitly use knowledge of the simulator's equations, i.e. mechanistic emulators based on Gaussian Processes, with purely data-driven emulators using matrix factorization. Our results suggest that in many urban applications, naive data-driven emulation outperforms mechanistic emulation. Nevertheless, we discuss scenarios in which we think that mechanistic emulation might be favorable for i) extrapolation in time and ii) dealing with sparse and unevenly sampled data. We also provide many references to advances in the field of Machine Learning that have not yet permeated into the Bayesian environmental science community. arXiv:1609.08395v2 [stat.ME]

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models

Carbajal

Leito

Albert

et al. 2017

Environmental Modelling & Software

View full text Add to dashboard Cite

show abstract

“…Reducing the internal precision of numerical computation for a same final resolution is becoming an attractive solution to the processing of data whose quantity is increasing at exploding rates 8 and implying heavy expenses in power consumption. Recently proposed linear solvers have opted for such a reduction in the execution of standard algebraic methods.…”

Section: Context and Goalmentioning

confidence: 99%

Coarse‐arithmetic coordinate descent for the resolution of semidefinite linear systems

Thao

Rzepka

2021

Numerical Linear Algebra App

View full text Add to dashboard Cite

We propose an inexact coordinate descent method to solve a consistent equation of the type Ax = b where A is a real symmetric and positive semidefinite matrix. The admissible range of inexactitude allows to reduce every multiplication present in the computation to a scaling by a signed power of 2 for the sake of hardware simplification. Although the resulting descent is nonideal, the numerical experiments show that its rate of convergence remains close to that of exact coordinate descent, whether the coordinate selection is cyclic or random.Meanwhile, our algorithm outperforms both methods with an additional low complexity "weak greedy" selection of the coordinates, also based on scaling by signed powers of 2. Our method is based on an advanced use of varying relaxation coefficients in the Gauss-Seidel iteration, with special theoretical considerations when A is singular.

show abstract

“…Although many scientific applications use double-precision floating-point by default, this accuracy is not always required. Instead, low-and mixed-precision arithmetic has been very effective for the computation of inverse matrix roots [182], or solving systems of linear equations [392][393][394][395]. Driven by the growing popularity of artificial neural networks that can be evaluated and trained with reduced precision, hardware accelerators have gained improved low-precision computing support.…”

Section: B Approximate Computingmentioning

confidence: 99%

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

Kühne,

Iannuzzi,

Del Ben

et al. 2020

Preprint

View full text Add to dashboard Cite

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

show abstract

A fast, hybrid, power-efficient high-precision solver for large linear systems based on low-precision hardware

Cited by 9 publications

References 7 publications

Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models

Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models

Coarse‐arithmetic coordinate descent for the resolution of semidefinite linear systems

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

Contact Info

Product

Resources

About