Abstract
In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon–nucleon (NN) scattering amplitudes with the wave-packet continuum discretisation method (WPCD). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit to explore the benefits of this inherent parallelism. From a theoretical perspective, the WPCD method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLOopt interaction to demonstrate that WPCD enables efficient computation of NN scattering amplitudes provided one can tolerate an averaged method error of 1–5 mb in the total cross section at scattering energies 0–350 MeV in the laboratory frame of reference. Considering only scattering energies ∼40–350 MeV, we find a smaller method error of ≲ 1–2 mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the WPCD method will be offset by the increased size of the resulting discretisation mesh. In practice, a GPU-implementation is mainly advantageous for matrices that fit in the fast on-chip shared memory. We find that WPCD is a promising method for computationally efficient, statistical analyses of nuclear interactions from effective field theory, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.
Highlights
We let NQ denote the number of quadrature points in the case of the MI method, while NWP denotes the number of wave packets in the case of the wave-packet continuum discretisation method (WPCD) method
We find that the root-meansquare error (RMSE) for WPCD with scattering energies corresponding to laboratory kinetic energies 40 ≤ Tlab ≤ 350 MeV remains fairly constant at ∼ 2.0 mb when using NWP = 16
For WPCD we can only vary the number of wave packets NWP while for MI we can vary both NQ and nE, i.e. the number quadrature points and the number of interpolation points or on-shell energies, respectively
Summary
A large portion of interaction-potential models currently applied in ab initio manynucleon calculations are constructed using ideas from chiral effective field theory (χEFT) [1, 2, 3, 4]. There are essentially three approaches for improving computational efficiency and speed of a computational procedure: i) develop improved numerical methods and algorithms tailored to the physical model at hand and its application, ii) use specific hardware, e.g. a faster CPU, increased memory bandwidth, or parallel architectures such as in a graphics processing unit (GPU) to better handle some of the most dominant computational procedures of the model, or iii) replace any computationally expensive model evaluations with a fast, as well as sufficiently accurate and precise, surrogate model, i.e. an emulator, which mimics the original model output This latter approach is very interesting and in particular eigenvector continuation (EC) [11, 12] applied to emulate NN-scattering amplitudes [13, 14] shows great promise, uncertainty quantification is yet to be explored. Throughout this work we will compare the efficiency and accuracy of the WPCD method, presented in Sec. 3.2, to a set of numerically exact results obtained using the MI method presented below
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