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IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments. MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically. Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.
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Effects of Different Closure Choices in Core-collapse Supernova Simulations
Abstract The two-moment method is widely used to approximate the full neutrino transport equation in core-collapse supernova (CCSN) simulations, and different closures lead to subtle differences in the simulation results. In this paper, we compare the effects of closure choices on various physical quantities in 1D and 2D time-dependent CCSN simulations with our multigroup radiation hydrodynamics code Fornax. We find that choices of the third-order closure relations influence the time-dependent simulations only slightly. Choices of the second-order closure relation have larger consequences than choices of the third-order closure, but these are still small compared to the remaining variations due to ambiguities in some physical inputs such as the nuclear equation of state. We also find that deviations in Eddington factors are not monotonically related to deviations in physical quantities, which means that simply comparing the Eddington factors does not inform one concerning which closure is better.
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- Award ID(s):
- 1804048
- PAR ID:
- 10393622
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 943
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 78
- Size(s):
- Article No. 78
- Sponsoring Org:
- National Science Foundation
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