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Learning transport processes with machine intelligence. Sci Rep 2022; 12:11709. [PMID: 35810177 PMCID: PMC9271097 DOI: 10.1038/s41598-022-15416-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 06/23/2022] [Indexed: 11/28/2022] Open
Abstract
Transport processes ruled by complex micro-physics and impractical to theoretical investigation may exhibit emergent behavior describable by mathematical expressions. Such information, while implicitly contained in the results of microscopic-scale numerical simulations close to first principles or experiments is not in a form suitable for macroscopic modelling. Here we present a machine learning approach that leverages such information to deploy micro-physics informed transport flux representations applicable to a continuum mechanics description. One issue with deep neural networks, arguably providing the most generic of such representations, is their noisiness which is shown to break the performance of numerical schemes. The matter is addressed and a methodology suitable for schemes characterised by second order convergence rate is presented. The capability of the methodology is demonstrated through an idealized study of the long standing problem of heat flux suppression relevant to fusion and cosmic plasmas. Symbolic representations, although potentially less generic, are straightforward to use in numerical schemes and theoretical analysis, and can be even more accurate as shown by the application to the same problem of an advanced symbolic regression tool. These results are a promising initial step to filling the gap between micro and macro in this important area of modeling.
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Sutcliffe GD, Pearcy JA, Johnson TM, Adrian PJ, Kabadi NV, Pollock B, Moody JD, Petrasso RD, Li CK. Experiments on the dynamics and scaling of spontaneous-magnetic-field saturation in laser-produced plasmas. Phys Rev E 2022; 105:L063202. [PMID: 35854613 DOI: 10.1103/physreve.105.l063202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
In laser-produced high-energy-density plasmas, large-scale strong magnetic fields are spontaneously generated by the Biermann battery effects when temperature and density gradients are misaligned. Saturation of the magnetic field takes place when convection and dissipation balance field generation. While theoretical and numerical modeling provide useful insight into the saturation mechanisms, experimental demonstration remains elusive. In this letter, we report an experiment on the saturation dynamics and scaling of Biermann battery magnetic field in the regime where plasma convection dominates. With time-gated charged-particle radiography and time-resolved Thomson scattering, the field structure and evolution as well as corresponding plasma conditions are measured. In these conditions, the spatially resolved magnetic fields are reconstructed, leading to a picture of field saturation with a scaling of B∼1/L_{T} for a convectively dominated plasma, a regime where the temperature gradient scale (L_{T}) exceeds the ion skin depth.
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Affiliation(s)
- G D Sutcliffe
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - J A Pearcy
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - T M Johnson
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - P J Adrian
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - N V Kabadi
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - B Pollock
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - J D Moody
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - R D Petrasso
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - C K Li
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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