A maximum likelihood method for linking particle-in-cell and Monte-Carlo transport simulations

Bowers, K. J.; DeVolder, B.G.; Yin, L.; Kwan, Thomas J. T.

doi:10.1016/j.cpc.2004.06.042

Cited by 8 publications

(16 citation statements)

References 2 publications

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“…The distribution of φ was modelled with a Gaussian mixture model (GMM) [22,23] to determine the number of minima, their locations, and widths. This approach models the total distribution as a sum of univariate Gaussian distributions.…”

Section: Discussionmentioning

confidence: 99%

Can the protonation state of histidine residues be determined from molecular dynamics simulations?

Uranga

Mikulskis

Genheden

et al. 2012

Computational and Theoretical Chemistry

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Section: Discussionmentioning

confidence: 99%

Can the protonation state of histidine residues be determined from molecular dynamics simulations?

Uranga

Mikulskis

Genheden

et al. 2012

Computational and Theoretical Chemistry

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“…The proposed CR strategy exactly conserves local (per cell) charge, momentum, and energy, satisfies Gauss' law everywhere, is massively parallel, communication-avoiding, locality-aware, and asynchronous by construction (except for the mass-matrix solve step), and only synchronizes and checkpoints compressed data. It is worth pointing out that we are not the first ones to realize the potential of GM PDF reconstruction in PIC algorithms, with various authors having used it in the past for diagnostics [15], to couple with other physical processes [16], or, more related to this study, for Gaussian-to-Gaussian remapping in 1D-1V phase-space to eliminate Gaussian-shape distortion in a finite-mass-method-based Vlasov-Poisson algorithm [17]. However, to our knowledge, this is the first application of an adaptive GM algorithm for particle data compression in CR of PIC simulations.…”

Section: Introductionmentioning

confidence: 99%

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

Chen,

Chacon,

Nguyen

2020

Preprint

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We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm features a particle compression stage and a particle reconstruction stage, where a continuum particle distribution function (PDF) is constructed and resampled, respectively. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. We demonstrate the algorithm using a recently developed exactly energy-and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

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“…Although in the present example we only tested the sampling of basins in two and four dimensions, it is known [39] that Gaussian mixture models can extend to a few more dimensions. In analogy to related developments to the metadynamics methodology [61], it should be possible to use multiple GAMUS simulations in a Hamiltonian replica exchange simulation.…”

Section: Resultsmentioning

confidence: 99%

“…To minimize round-off errors, this Cholesky factor is updated with a row-wise economy QR factorization [39] based on a Givens rotation [67]. We further imposed constraints on the variance-covariance matrix [46], such that the Gaussians would not shrink to less than one degree in any direction.…”

mentioning

confidence: 99%

Gaussian-Mixture Umbrella Sampling

2009

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We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multi-dimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multi-dimensional reaction coordinates. To illustrate GAMUS, we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate).

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A maximum likelihood method for linking particle-in-cell and Monte-Carlo transport simulations

Cited by 8 publications

References 2 publications

Can the protonation state of histidine residues be determined from molecular dynamics simulations?

Can the protonation state of histidine residues be determined from molecular dynamics simulations?

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

Gaussian-Mixture Umbrella Sampling

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