Model reduction methods for nuclear emulators

Melendez, J. A.; Drischler, C.; Furnstahl, R. J.; Garcia, A.J.; Zhang, X.

doi:10.1088/1361-6471/ac83dd

Cited by 19 publications

(5 citation statements)

References 89 publications

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“…We must now implement the constraint j β j = 1, which is performed here by a Lagrange multiplier λ mimicking a variational approach (see Ref. [19] for details):…”

Section: Discussionmentioning

confidence: 99%

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Wave function-based emulation for nucleon-nucleon scattering in momentum space

Garcia¹,

Drischler²,

Furnstahl³

et al. 2023

Preprint

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Emulators for low-energy nuclear physics can provide fast & accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (NN) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (np) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

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“…We must now implement the constraint j β j = 1, which is performed here by a Lagrange multiplier λ mimicking a variational approach (see Ref. [19] for details):…”

Section: Discussionmentioning

confidence: 99%

“…For general overviews of the literature on PMOR techniques and their applications, we refer the reader to Refs. [19,20]. A pedagogical introduction to projection-based emulators for both scattering and bound-state calculations, including interactive, open-source Python code, can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

Wave function-based emulation for nucleon-nucleon scattering in momentum space

Garcia¹,

Drischler²,

Furnstahl³

et al. 2023

Preprint

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“…This technique is powerful yet simple and is based on exploiting information contained in eigenvectors in the training regime. Recent work [38,39] has established EC as a particular reduced-basis (RB) method that falls within a larger class of model-order reduction (MOR) techniques.…”

Section: Fast Volume Extrapolationmentioning

confidence: 99%

Efficient few-body calculations in finite volume

König

2023

J. Phys.: Conf. Ser.

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Simulating quantum systems in a finite volume is a powerful theoretical tool to extract information about them. Real-world properties of the system are encoded in how its discrete energy levels change with the size of the volume. This approach is relevant not only for nuclear physics, where lattice methods for few- and many-nucleon states complement phenomenological shell-model descriptions and ab initio calculations of atomic nuclei based on harmonic oscillator expansions, but also for other fields such as simulations of cold atomic systems. This contribution presents recent progress concerning finite-volume simulations of few-body systems. In particular, it discusses details regarding the efficient numerical implementation of separable interactions and it presents eigenvector continuation as a method for performing robust and efficient volume extrapolations.

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“…This computational challenge has motivated many of the recent efforts by the nuclear theory community in the development and adoption of emulators to accelerate computation speed with a minimal precision loss [23][24][25][26][27][28][29][30][31][32][33][34][35]. In this work we explore the application of one such class of emulators, the Reduced Basis Method (RBM) [36][37][38], which falls under the umbrella of the general Reduced Order Models (ROM) techniques [39,40].…”

Section: Introductionmentioning

confidence: 99%

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

et al. 2023

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A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method (RBM)—a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build—using only 100 evaluations of the high-fidelity model—is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver. Besides the analysis of the posterior distribution of parameters, we present model calculations for masses and radii with properly estimated uncertainties. We also analyze the model correlation between the slope of the symmetry energy L and the neutron skin of 48Ca and 208Pb. The straightforward implementation and outstanding performance of the RBM makes it an ideal tool for assisting the nuclear theory community in providing reliable estimates with properly quantified uncertainties of physical observables. Such uncertainty quantification tools will become essential given the expected abundance of data from the recently inaugurated and future experimental and observational facilities.

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Model reduction methods for nuclear emulators

Cited by 19 publications

References 89 publications

Wave function-based emulation for nucleon-nucleon scattering in momentum space

Wave function-based emulation for nucleon-nucleon scattering in momentum space

Efficient few-body calculations in finite volume

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

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