PDFO: A Cross-Platform Package for Powell's Derivative-Free Optimization Solvers

Ragonneau, Tom M.; Zhang, Zaikun

doi:10.48550/arxiv.2302.13246

Cited by 2 publications

(2 citation statements)

References 60 publications

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“…The penalty method was used because the field strength constraints are 'soft constraints'-they do not need to be satisfied exactly. Powell's BOBYQA algorithm [50] within the Python package PDFO [51] was used to solve equation (24). BOBYQA is a derivative-free trust region method that uses local quadratic approximations of the objective to make progress towards a minimum.…”

Section: Methodsmentioning

confidence: 99%

Direct Optimization of Fast-Ion Confinement in Stellarators

Bindel

Landreman

Padidar

2023

Plasma Phys. Control. Fusion

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Confining energetic ions such as alpha particles is a prime concern in the design of stellarators. However, directly measuring alpha confinement through numerical simulation of guiding-center trajectories has been considered to be too computationally expensive and noisy to include in the design loop, and instead has been most often used only as a tool to assess stellarator designs post hoc. In its place, proxy metrics, simplified measures of confinement, have often been used to design configurations because they are computationally more tractable and have been shown to be effective. Despite the success of proxies, their correlation with direct trajectory calculations is known to be imperfect. In this study, we optimize stellarator designs for improved alpha particle confinement without the use of proxy metrics. In particular, we numerically optimize an objective function that measures alpha particle losses by simulating alpha particle trajectories. While this method is computationally expensive, we find that it can be used successfully to generate configurations with low losses.

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Section: Methodsmentioning

confidence: 99%

Direct Optimization of Fast-Ion Confinement in Stellarators

Bindel

Landreman

Padidar

2023

Plasma Phys. Control. Fusion

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“…It is an unrestrained parameter fi�ng algorithm that does not need gradients. We used the implementa�on in the python package PDFO 1.2 63 . The default convergence criteria were used, and the ini�al guessing radius parameter rhobeg was set to 0.01.…”

Section: Fi�ng Algorithmmentioning

confidence: 99%

An atomic radii set and Generalized Born implicit solvation model trained using explicit water solvation free energy data

Wang,

Tian,

Pincay

et al. 2024

Preprint

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Compared with the other common implicit and explicit water models, Generalized Born (GB) models can provide a fast approximation of solvation free energy that is reasonably accurate but fast enough to use in molecular dynamics (MD) simulations. This enhances conformational sampling of the solute molecules, and also can be a valuable component of multi-scale simulations. We previously developed the GB-Neck2 model, which exhibited improved secondary structure balance and was used to successfully fold a series of small proteins. More recent simulations using GB-Neck2 with updated protein models suggest that α-helices remain somewhat over-stabilized. Here, we develop a more self-consistent model, retraining both the intrinsic solvation radii as well as the GB model parameters, using the solvation free energies of an explicit water model as training references. The new radii set, named MIRO, when used with the GBNSR6 implicit solvent model leads to improved reproduction of solvation free energies calculated in explicit water. The new GB-Neck3 model shows a good balance of secondary structures: the stability of β-sheets is improved, while the previously over-stabilized α-helices became less favorable, as expected. GB-Neck3 and MIRO radii should extend the range of problems accessible to biomolecular simulation.

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PDFO: A Cross-Platform Package for Powell's Derivative-Free Optimization Solvers

Cited by 2 publications

References 60 publications

Direct Optimization of Fast-Ion Confinement in Stellarators

Direct Optimization of Fast-Ion Confinement in Stellarators

An atomic radii set and Generalized Born implicit solvation model trained using explicit water solvation free energy data

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