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Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification

MPS-Authors
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Schwenk,  A.
Division Prof. Dr. Klaus Blaum, MPI for Nuclear Physics, Max Planck Society;

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1909.08446.pdf
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Citation

König, S., Ekström, A., Hebeler, K., Lee, D., & Schwenk, A. (2020). Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification. Physics Letters B, 810: 135814. doi:10.1016/j.physletb.2020.135814.


Cite as: http://hdl.handle.net/21.11116/0000-0007-7387-F
Abstract
First principles calculations of atomic nuclei based on microscopic nuclear forces derived from chiral effective field theory (EFT) have blossomed in the past years. A key element of such ab initio studies is the understanding and quantification of systematic and statistical errors arising from the omission of higher-order terms in the chiral expansion as well as the model calibration. While there has been significant progress in analyzing theoretical uncertainties for nucleon-nucleon scattering observables, the generalization to multi-nucleon systems has not been feasible yet due to the high computational cost of evaluating observables for a large set of low-energy couplings. In this Letter we show that a new method called eigenvector continuation (EC) can be used for constructing an efficient and accurate emulator for nuclear many-body observables, thereby enabling uncertainty quantification in multi-nucleon systems. We demonstrate the power of EC emulation with a proof-of-principle calculation that lays out all correlations between bulk ground-state observables in the few-nucleon sector. On the basis of ab initio calculations for the ground-state energy and radius in 4He, we demonstrate that EC is more accurate and efficient compared to established methods like Gaussian processes.