4,458 research outputs found
Differentiable Programming Tensor Networks
Differentiable programming is a fresh programming paradigm which composes
parameterized algorithmic components and trains them using automatic
differentiation (AD). The concept emerges from deep learning but is not only
limited to training neural networks. We present theory and practice of
programming tensor network algorithms in a fully differentiable way. By
formulating the tensor network algorithm as a computation graph, one can
compute higher order derivatives of the program accurately and efficiently
using AD. We present essential techniques to differentiate through the tensor
networks contractions, including stable AD for tensor decomposition and
efficient backpropagation through fixed point iterations. As a demonstration,
we compute the specific heat of the Ising model directly by taking the second
order derivative of the free energy obtained in the tensor renormalization
group calculation. Next, we perform gradient based variational optimization of
infinite projected entangled pair states for quantum antiferromagnetic
Heisenberg model and obtain start-of-the-art variational energy and
magnetization with moderate efforts. Differentiable programming removes
laborious human efforts in deriving and implementing analytical gradients for
tensor network programs, which opens the door to more innovations in tensor
network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted
for publication in PRX. Source code available at
https://github.com/wangleiphy/tensorgra
Composite Rotor Blade Design Optimization for Vibration Reduction with Aeroelastic Constraints
AbstractThe paper presents an analytical study of the helicopter rotor vibratory load reduction design optimization with aeroelastic stability constraints. The composite rotor blade is modeled by beam type finite elements, and warping deformation is taken into consideration for 2 dimension analysis, while the one-dimension nonlinear differential equations of blade motion are formulated via Hamilton's principle. The rotor hub vibratory loads is chosen as the objective function, while rotor blade section construction parameter, composite material ply structure and blade tip swept angle as the design variables, and autorotation inertia, natural frequency and aeroelastic stability as the constraints. A 3 bladed rotor is designed, as an example, based on the vibratory hub load reduction optimization process with swept tip angle and composite material. The calculating results show a 24. 9%-33% reduction of 3/rev hub loads in comparison with the base-line rotor
Conserved quantities for asymptotically AdS spacetimes in quadratic curvature gravity in terms of a rank-4 tensor
We investigate the conserved quantities associated to Killing isometries for
asymptotically AdS spacetimes within the framework of quadratic-curvature
gravity. By constructing a rank-4 tensor possessing the same index symmetries
as the ones of the Riemann tensor, we propose a 2-form potential resembling the
Noether one for quadratic-curvature gravity. Such a potential is compared with
the results via other methods existing in the literature to establish the
equivalence. Then this potential is adopted to define conserved quantities of
asymptotically AdS spacetimes. As applications, we explicitly compute the mass
of static spherically-symmetric spacetimes, as well as the mass and the angular
momentum for rotating spacetimes, such as the four(higher)-dimensional Kerr-AdS
black holes and black strings embedded in quadratic-curvature gravities.
Particularly, we emphasize the conserved charges of Einstein-Gauss-Bonnet, Weyl
and critical gravities, together with the ones for the asymptotically AdS
solutions satisfying vacuum Einstein field equations.Comment: 50 pages, no figures, accepted by PR
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