Greedy Emulators for Nuclear Two-Body Scattering
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| Format: | Preprint |
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2025
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| _version_ | 1866909720075304960 |
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| author | Maldonado, J. M. Drischler, C. Furnstahl, R. J. Mlinarić, P. |
| author_facet | Maldonado, J. M. Drischler, C. Furnstahl, R. J. Mlinarić, P. |
| contents | Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. In this paper, we develop, implement, and test two model-driven emulators based on (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples ("snapshots") for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires much fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Greedy Emulators for Nuclear Two-Body Scattering Maldonado, J. M. Drischler, C. Furnstahl, R. J. Mlinarić, P. Nuclear Theory High Energy Physics - Phenomenology Nuclear Experiment Data Analysis, Statistics and Probability Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. In this paper, we develop, implement, and test two model-driven emulators based on (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples ("snapshots") for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires much fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems. |
| title | Greedy Emulators for Nuclear Two-Body Scattering |
| topic | Nuclear Theory High Energy Physics - Phenomenology Nuclear Experiment Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2504.06092 |