Nested sampling for physical scientists

Ashton, G.; Bernstein, Noam; Buchner, Johannes; Chen, Xi; Csänyi, Gábor; Fowlie, Andrew; Feroz, Farhan; Griffiths, Matthew; Handley, Will; Habeck, Michael; Higson, Edward; Hobson, M.; Lasenby, A.; Parkinson, David; Partay, L.B.; Pitkin, M.; Schneider, Doris; Speagle, Joshua S.; South, Leah F.; Veitch, J.; Wacker, Philipp; Wales, David J.; Yallup, D. P.

doi:10.1038/s43586-022-00121-x

Cited by 64 publications

(46 citation statements)

References 239 publications

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“…NS differs from typical MCMC samplers as it is primarily an integration algorithm, hence by definition has to overcome a lot of the difficulties MCMC samplers face in multimodal problems. A recent community review of its various applications in the physical sciences, and various implementations of the algorithm has been presented in [41].…”

Section: Nested Sampling For Event Generationmentioning

confidence: 99%

Exploring phase space with nested sampling

et al. 2022

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We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to the integration of partonic scattering cross sections and the generation of individual events distributed according to the corresponding squared matrix element. As a first concrete example we consider gluon scattering processes into 3-, 4- and 5-gluon final states and compare the performance with established sampling techniques. Starting from a flat prior distribution Nested Sampling outperforms the Vegas algorithm and achieves results comparable to a dedicated multi-channel importance sampler. We outline possible approaches to combine Nested Sampling with non-flat prior distributions to further reduce the variance of integral estimates and to increase unweighting efficiencies.

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Section: Nested Sampling For Event Generationmentioning

confidence: 99%

Exploring phase space with nested sampling

et al. 2022

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“…The configuration space of the Jagla model was explored using the nested sampling (NS) method. NS is a Bayesian inference method developed by Skilling 43,44 that has been adapted to sample the potential energy landscape of atomistic systems. 33,[45][46][47] NS is a ''top-down'' approach, starting from randomly generated configurations representing the high enthalpy region (or the high energy in case of the canonical ensemble) of the phase-space, propagating towards the global minimum through a series of iterative steps which shrink the available phase space by a constant fraction.…”

Section: Simulation Detailsmentioning

confidence: 99%

Stability of the high-density Jagla liquid in 2D: sensitivity to parameterisation

Partay

Hantal

2022

Soft Matter

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“…In the current work we aim to evaluate the performance of carbon potentials and calculate their pressure-temperature phase diagram, by performing an exhaustive and predictive sampling of the entire potential energy surface, using the nested sampling technique. [38,39] Nested sampling (NS) was first introduced by John Skilling in the area of Bayesian statistics, [40,41] later taken up by various research fields [39] and adapted to sample the potential energy surface of atomistic systems [38,42]. The main advantages of NS are that it automatically generates the thermodynamically relevant structures without any prior knowledge of, e.g., crystalline structures, and it provides unique and easy access to the notoriously elusive partition function.…”

Section: Introductionmentioning

confidence: 99%

Exploring the configuration space of elemental carbon with empirical and machine learned interatomic potentials

Marchant

Miguel

Karasulu

et al. 2023

Preprint

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In the present work we detail how the many-body potential energy landscape of elemental carbon, as described by interatomic potentials, can be explored by utilising the nested sampling algorithm, allowing the calculation of their pressure-temperature phase diagram up to high pressures. We present a comparison of four interatomic potential models: Tersoff, EDIP, GAP-20 and its recently updated version, GAP-20U. Our evaluation is focused on their macroscopic properties, particularly on their melting transition and on identifying thermodynamically stable solid structures up to at least 100 GPa. The studied models all form graphite structures upon freezing at lower pressure, then the diamond structure as the pressure increases. In the cases of the Tersoff, EDIP and GAP-20U potentials we were able to locate the transition between these phases. We placed particular focus on the state-of-the-art machine-learned models, the GAP-20 and GAP-20U, and calculated their phase diagrams up to 1 and 0.1 TPa, respectively, to evaluate their predictive capabilities well outside of the models’ fitting range. The phase diagrams of the GAP models showed remarkably good agreement with the experimental phase diagram up to 200 GPa. However, we found that the accuracy of the models’ descriptions of graphite was adversely affected by the relative stability of phases with incorrect layer spacing. By adding a suitable selection of graphite structures to the GAP training set and re-training the model, we have derived an improved model — referred to as the GAP-20U+gr — that suppresses erroneous local minima in the graphitic energy landscape. At extreme high pressure nested sampling identified two novel stable solid structures in the GAP-20 model, a strained diamond structure above 270 GPa and a strained hexagonal-close-packed structure above 890 GPa. However, the stability of these two phases were not confirmed by DFT calculations, highlighting potential routes to further improve the GAP model.

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Nested sampling for physical scientists

Abstract: How to cite:Please refer to published version for the most recent bibliographic citation information.

Cited by 64 publications

References 239 publications

Exploring phase space with nested sampling

Exploring phase space with nested sampling

Stability of the high-density Jagla liquid in 2D: sensitivity to parameterisation

Exploring the configuration space of elemental carbon with empirical and machine learned interatomic potentials

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