Incorporating Quantities of Interests into Low-Rank Tensor Decompositions
Technical talk on low-rank decompositions of tensors used for data compression
Dunlavy, Daniel Michael [Sandia National Laborator↗
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Multigroup Thermal Radiation Transport with Tensor Trains
We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than 100× and speedups exceeding 2×. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as 7. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.
79 ASTRONOMY AND ASTROPHYSICS↗
Dielectric tensor in Vlasov plasmas near cyclotron harmonics.
Dielectric tensor in relativistic Vlasov plasma in electron cyclotron harmonic resonance region
PLASMA DISPERSION↗
The dielectric tensor near cyclotron harmonics
Dielectric tensor elements derived for study of wave dispersion near cyclotron harmonics for Alouette satellite
CYCLOTRON FREQUENCY↗
Gradient-elastic tensor in sodium chloride and sodium bromide.
Gradient-elastic tensor of ions in sodium chloride and sodium bromide crystals determined from effects of static elastic strain on nuclear magnetic resonance
NUCLEAR MAGNETIC RESONANCE↗
Tensor electrical conductivity of atmospheric cesium-seeded argon.
Third Chapman-Enskog approximation to tensor electrical conductivity of partially ionized gas applied to two conductivity mixture rules for atmospheric cesium seeded argon
ELECTRIC CONDUCTIVITY↗
Schiff's proposed gyroscope experiment as a test of the scalar-tensor theory of general relativity.
Schiff gyroscope experiment as test of Brans- Dicke scalar tensor general relativity theory, deriving expression for gyroscope momentum precession
Oconnell, R. F.↗
Effective dielectric tensor and propagation constant of plane waves in a random anisotropic medium.
Wave propagation in turbulent magnetoactive plasma, deriving dielectric tensor operator through Green function
Liu, C. H.↗
Gravitational radiation in the limit of high frequency. II - Nonlinear terms and the effective stress tensor.
HF vacuum gravitational field expansion, discussing nonlinear terms and effective stress tensor for gravitational waves localized energy
Isaacson, R. A.↗
Mobility tensor for a strongly turbulent Lorentz gas in a magnetic field.
Perpendicular mobility tensor for strongly turbulent Lorentz gas in magnetic field, linearizing terms in Fourier analyzed momentum equation
Frank, E. N.↗
Cauchy problem in the scalar-tensor gravitational theory.
Cauchy problem for scalar-tensor gravitational theory, splitting field equations into initial value equations and evolution equations
Cocke, W. J.↗
Cosmic-ray diffusion tensor and its variation observed with Mariner 4.
Interplanetary magnetic field power spectra from Mariner 4 spacecraft data used to determine cosmic ray diffusion tensor and variation in interplanetary space
Coleman, P. J., Jr.↗
Report on the investigation of Mach's principle in the scalar-tensor theory of gravity.
Mach principle in scalar-tensor gravitation theory, discussing self energy calculations in canonical formalism for solitary neutral and charged point particles
Toton, E.↗
Dipole shielding tensor
Dipole shielding tensor of atom in arbitrary time dependent field, giving conditions for general variational calculations yielding results
Epstein, S. T.↗
A compact method for symbolic computation of the Riemann tensor
Riemann tensor symbolic computation by compact method using differential forms, discussing advantages due to antisymmetry
Harrison, G. H.↗
Lattice-vibrational properties of chromium in the harmonic approximation on the basis of the tensor model
Chromium lattice vibrational properties based on fourth-nearest-neighbor tensor force model, obtaining agreement with inelastic neutron diffraction data and elastic constants
Feldman, J. L.↗
Scalar-tensor theory in canonical form. I
Scalar-tensor theory in canonical form, discussing neutral particle and electron self energy problem
Toton, E. T.↗