2,138 research outputs found
Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution
Convolutional neural networks have recently demonstrated high-quality
reconstruction for single-image super-resolution. In this paper, we propose the
Laplacian Pyramid Super-Resolution Network (LapSRN) to progressively
reconstruct the sub-band residuals of high-resolution images. At each pyramid
level, our model takes coarse-resolution feature maps as input, predicts the
high-frequency residuals, and uses transposed convolutions for upsampling to
the finer level. Our method does not require the bicubic interpolation as the
pre-processing step and thus dramatically reduces the computational complexity.
We train the proposed LapSRN with deep supervision using a robust Charbonnier
loss function and achieve high-quality reconstruction. Furthermore, our network
generates multi-scale predictions in one feed-forward pass through the
progressive reconstruction, thereby facilitates resource-aware applications.
Extensive quantitative and qualitative evaluations on benchmark datasets show
that the proposed algorithm performs favorably against the state-of-the-art
methods in terms of speed and accuracy.Comment: This work is accepted in CVPR 2017. The code and datasets are
available on http://vllab.ucmerced.edu/wlai24/LapSRN
Semi-supervised Local Cluster Extraction by Compressive Sensing
Local clustering problem aims at extracting a small local structure inside a
graph without the necessity of knowing the entire graph structure. As the local
structure is usually small in size compared to the entire graph, one can think
of it as a compressive sensing problem where the indices of target cluster can
be thought as a sparse solution to a linear system. In this paper, we propose a
new semi-supervised local cluster extraction approach by applying the idea of
compressive sensing based on two pioneering works under the same framework. Our
approves improves the existing works by making the initial cut to be the entire
graph and hence overcomes a major limitation of existing works, which is the
low quality of initial cut. Extensive experimental results on multiple
benchmark datasets demonstrate the effectiveness of our approach
Analytical approximations to charged black hole solutions in Einstein-Maxwell-Weyl gravity
The Homotopy Analysis Method (HAM) is a useful method to derive analytical
approximate solutions of black holes in modified gravity theories. In this
paper, we study the Einstein-Weyl gravity coupled with Maxwell field, and
obtain analytical approximation solutions for charged black holes by using the
HAM. It is found that the analytical approximate solutions are sufficiently
accurate in the entire spacetime outside the black hole's event horizon, and
also consistent with numerical ones for charged black holes in the
Einstein-Maxwell-Weyl gravity.Comment: 17 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2308.0350
(4RS)-Methyl 4-cyano-4-cyclohexyl-4-phenylbutanoate
In the crystal structure of the title compound, C18H23NO2, there are only van der Waals interactions present. The cyclohexyl ring has a chair conformation. The longer axes of the displacement parameters of the non-H atoms forming the ethylmethylcarboxylate skeleton are perpendicular to the plane through the non-H atoms of this skeleton
A cusp-capturing PINN for elliptic interface problems
In this paper, we propose a cusp-capturing physics-informed neural network
(PINN) to solve discontinuous-coefficient elliptic interface problems whose
solution is continuous but has discontinuous first derivatives on the
interface. To find such a solution using neural network representation, we
introduce a cusp-enforced level set function as an additional feature input to
the network to retain the inherent solution properties; that is, capturing the
solution cusps (where the derivatives are discontinuous) sharply. In addition,
the proposed neural network has the advantage of being mesh-free, so it can
easily handle problems in irregular domains. We train the network using the
physics-informed framework in which the loss function comprises the residual of
the differential equation together with certain interface and boundary
conditions. We conduct a series of numerical experiments to demonstrate the
effectiveness of the cusp-capturing technique and the accuracy of the present
network model. Numerical results show that even using a one-hidden-layer
(shallow) network with a moderate number of neurons and sufficient training
data points, the present network model can achieve prediction accuracy
comparable with traditional methods. Besides, if the solution is discontinuous
across the interface, we can simply incorporate an additional supervised
learning task for solution jump approximation into the present network without
much difficulty
An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications
A new and efficient neural-network and finite-difference hybrid method is
developed for solving Poisson equation in a regular domain with jump
discontinuities on embedded irregular interfaces. Since the solution has low
regularity across the interface, when applying finite difference discretization
to this problem, an additional treatment accounting for the jump
discontinuities must be employed. Here, we aim to elevate such an extra effort
to ease our implementation by machine learning methodology. The key idea is to
decompose the solution into singular and regular parts. The neural network
learning machinery incorporating the given jump conditions finds the singular
solution, while the standard finite difference method is used to obtain the
regular solution with associated boundary conditions. Regardless of the
interface geometry, these two tasks only require supervised learning for
function approximation and a fast direct solver for Poisson equation, making
the hybrid method easy to implement and efficient. The two- and
three-dimensional numerical results show that the present hybrid method
preserves second-order accuracy for the solution and its derivatives, and it is
comparable with the traditional immersed interface method in the literature. As
an application, we solve the Stokes equations with singular forces to
demonstrate the robustness of the present method
A shallow physics-informed neural network for solving partial differential equations on surfaces
In this paper, we introduce a shallow (one-hidden-layer) physics-informed
neural network for solving partial differential equations on static and
evolving surfaces. For the static surface case, with the aid of level set
function, the surface normal and mean curvature used in the surface
differential expressions can be computed easily. So instead of imposing the
normal extension constraints used in literature, we write the surface
differential operators in the form of traditional Cartesian differential
operators and use them in the loss function directly. We perform a series of
performance study for the present methodology by solving Laplace-Beltrami
equation and surface diffusion equation on complex static surfaces. With just a
moderate number of neurons used in the hidden layer, we are able to attain
satisfactory prediction results. Then we extend the present methodology to
solve the advection-diffusion equation on an evolving surface with given
velocity. To track the surface, we additionally introduce a prescribed hidden
layer to enforce the topological structure of the surface and use the network
to learn the homeomorphism between the surface and the prescribed topology. The
proposed network structure is designed to track the surface and solve the
equation simultaneously. Again, the numerical results show comparable accuracy
as the static cases. As an application, we simulate the surfactant transport on
the droplet surface under shear flow and obtain some physically plausible
results
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