Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov–Maxwell equations
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Computer Science↗
Engineering topics
Huang, Juntao
Publications and source records attributed to Huang, Juntao.
Machine Learning Moment Closure Models for the Radiative Transfer Equation III: Enforcing Hyperbolicity and Physical Characteristic Speeds
This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation. In our previous work (Huang et al. in J Comput Phys 453:110941, 2022), we proposed an approach to learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, while the ML moment closure has better accuracy, it is not able to guarantee hyperbolicity and has issues with long time stability. In our second paper (Huang et al., in: Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, 2021. arXiv:2105.14410), we identified a symmetrizer which leads to conditions that enforce that the gradient based ML closure is symmetrizable hyperbolic and stable over long time. The limitation of this approach is that in practice the highest moment can only be related to four, or fewer, lower moments. In this paper, we propose a new method to enforce the hyperbolicity of the ML closure model. Motivated by the observation that the coefficient matrix of the closure system is a lower Hessenberg matrix, we relate its eigenvalues to the roots of an associated polynomial. Here, we design two new neural network architectures based on this relation. The ML closure model resulting from the first neural network is weakly hyperbolic and guarantees the physical characteristic speeds, i.e., the eigenvalues are bounded by the speed of light. The second model is strictly hyperbolic and does not guarantee the boundedness of the eigenvalues. Several benchmark tests including the Gaussian source problem and the two-material problem show the good accuracy, stability and generalizability of our hyperbolic ML closure model.
97 MATHEMATICS AND COMPUTING↗
Magnetic anisotropy in two-orbital models
Motivated by the recent first-principle discovery of giant perpendicular magnetic anisotropy (PMA) in Fe/III–V nitride thin films, we theoretically study magnetic crystalline anisotropy(MCA) in a series of lattices with trigonal symmetry. Due to the trigonal crystal field, MCA in these lattices is dominated by first-order perturbation of the spin–orbit coupling (SOC) in the atomic limit, instead of second-order in conventional transition metal materials. In particular, the proportionality between MCA and SOC is robust in Kagome and pyrochlore lattices due to the flat bands therein. While in triangle lattice the second-order relation is restored under the bandwidth effect. Furthermore, these findings give rise to a new understanding of magnetic anisotropy and provide a guide for the future hunting of high PMA materials.
36 MATERIALS SCIENCE↗
Machine learning moment closure models for the radiative transfer equation I: Directly learning a gradient based closure
In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for the radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. Finally, a variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model.
Computer science↗