84 research outputs found
Multiplicity of positive solutions for a fourth-order quasilinear singular differential equation
This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation
where , . We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold , such that if , then the problem admits at least one positive solution; while if , then the problem has no positive solution. In particular, there exist at least two positive solutions for
Evaluating Similitude and Robustness of Deep Image Denoising Models via Adversarial Attack
Deep neural networks (DNNs) have a wide range of applications in the field of
image denoising, and they are superior to traditional image denoising. However,
DNNs inevitably show vulnerability, which is the weak robustness in the face of
adversarial attacks. In this paper, we find some similitudes between existing
deep image denoising methods, as they are consistently fooled by adversarial
attacks. First, denoising-PGD is proposed which is a denoising model full
adversarial method. The current mainstream non-blind denoising models (DnCNN,
FFDNet, ECNDNet, BRDNet), blind denoising models (DnCNN-B, Noise2Noise,
RDDCNN-B, FAN), and plug-and-play (DPIR, CurvPnP) and unfolding denoising
models (DeamNet) applied to grayscale and color images can be attacked by the
same set of methods. Second, since the transferability of denoising-PGD is
prominent in the image denoising task, we design experiments to explore the
characteristic of the latent under the transferability. We correlate
transferability with similitude and conclude that the deep image denoising
models have high similitude. Third, we investigate the characteristic of the
adversarial space and use adversarial training to complement the vulnerability
of deep image denoising to adversarial attacks on image denoising. Finally, we
constrain this adversarial attack method and propose the L2-denoising-PGD image
denoising adversarial attack method that maintains the Gaussian distribution.
Moreover, the model-driven image denoising BM3D shows some resistance in the
face of adversarial attacks.Comment: 12 pages, 15 figure
A Review of Adversarial Attacks in Computer Vision
Deep neural networks have been widely used in various downstream tasks,
especially those safety-critical scenario such as autonomous driving, but deep
networks are often threatened by adversarial samples. Such adversarial attacks
can be invisible to human eyes, but can lead to DNN misclassification, and
often exhibits transferability between deep learning and machine learning
models and real-world achievability. Adversarial attacks can be divided into
white-box attacks, for which the attacker knows the parameters and gradient of
the model, and black-box attacks, for the latter, the attacker can only obtain
the input and output of the model. In terms of the attacker's purpose, it can
be divided into targeted attacks and non-targeted attacks, which means that the
attacker wants the model to misclassify the original sample into the specified
class, which is more practical, while the non-targeted attack just needs to
make the model misclassify the sample. The black box setting is a scenario we
will encounter in practice
Adversarial Training for Physics-Informed Neural Networks
Physics-informed neural networks have shown great promise in solving partial
differential equations. However, due to insufficient robustness, vanilla PINNs
often face challenges when solving complex PDEs, especially those involving
multi-scale behaviors or solutions with sharp or oscillatory characteristics.
To address these issues, based on the projected gradient descent adversarial
attack, we proposed an adversarial training strategy for PINNs termed by
AT-PINNs. AT-PINNs enhance the robustness of PINNs by fine-tuning the model
with adversarial samples, which can accurately identify model failure locations
and drive the model to focus on those regions during training. AT-PINNs can
also perform inference with temporal causality by selecting the initial
collocation points around temporal initial values. We implement AT-PINNs to the
elliptic equation with multi-scale coefficients, Poisson equation with
multi-peak solutions, Burgers equation with sharp solutions and the Allen-Cahn
equation. The results demonstrate that AT-PINNs can effectively locate and
reduce failure regions. Moreover, AT-PINNs are suitable for solving complex
PDEs, since locating failure regions through adversarial attacks is independent
of the size of failure regions or the complexity of the distribution
Image Denoising via Nonlinear Hybrid Diffusion
A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models
SaaFormer: Spectral-spatial Axial Aggregation Transformer for Hyperspectral Image Classification
Hyperspectral images (HSI) captured from earth observing satellites and
aircraft is becoming increasingly important for applications in agriculture,
environmental monitoring, mining, etc. Due to the limited available
hyperspectral datasets, the pixel-wise random sampling is the most commonly
used training-test dataset partition approach, which has significant overlap
between samples in training and test datasets. Furthermore, our experimental
observations indicates that regions with larger overlap often exhibit higher
classification accuracy. Consequently, the pixel-wise random sampling approach
poses a risk of data leakage. Thus, we propose a block-wise sampling method to
minimize the potential for data leakage. Our experimental findings also confirm
the presence of data leakage in models such as 2DCNN. Further, We propose a
spectral-spatial axial aggregation transformer model, namely SaaFormer, to
address the challenges associated with hyperspectral image classifier that
considers HSI as long sequential three-dimensional images. The model comprises
two primary components: axial aggregation attention and multi-level
spectral-spatial extraction. The axial aggregation attention mechanism
effectively exploits the continuity and correlation among spectral bands at
each pixel position in hyperspectral images, while aggregating spatial
dimension features. This enables SaaFormer to maintain high precision even
under block-wise sampling. The multi-level spectral-spatial extraction
structure is designed to capture the sensitivity of different material
components to specific spectral bands, allowing the model to focus on a broader
range of spectral details. The results on six publicly available datasets
demonstrate that our model exhibits comparable performance when using random
sampling, while significantly outperforming other methods when employing
block-wise sampling partition.Comment: arXiv admin note: text overlap with arXiv:2107.02988 by other author
Modeled Antarctic Precipitation. Part I: Spatial and Temporal Variability*
Surface snow accumulation is the primary mass input to the Antarctic ice sheets. As the dominant term among various components of surface snow accumulation (precipitation, sublimation/deposition, and snow drift), pre-cipitation is of particular importance in helping to assess the mass balance of the Antarctic ice sheets and their contribution to global sea level change. The Polar MM5, a mesoscale atmospheric model based on the fifth-generation Pennsylvania State University– NCAR Mesoscale Model, has been run for the period of July 1996 through June 1999 to evaluate the spatial and temporal variability of Antarctic precipitation. Drift snow effects on the redistribution of surface snow over Antarctica are also assessed with surface wind fields from Polar MM5 in this study. It is found that areas with large drift snow transport convergence and divergence are located around escarpment areas where there is considerable katabatic wind acceleration. It is also found that the drift snow transport generally diverges over most areas of East and West Antarctica with relatively small values. The use of the dynamic retrieval method (DRM) to calculate precipitation has been developed and verified for the Greenland ice sheet. The DRM is also applied to retrieve the precipitation over Antarctica from 1979 to 1999 in this study. Most major features in the spatial distribution of Antarctic accumulation are well capture
Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation
Variational level set method has become a powerful tool in image segmentation
due to its ability to handle complex topological changes and maintain
continuity and smoothness in the process of evolution. However its evolution
process can be unstable, which results in over flatted or over sharpened
contours and segmentation failure. To improve the accuracy and stability of
evolution, we propose a high-order level set variational segmentation method
integrated with molecular beam epitaxy (MBE) equation regularization. This
method uses the crystal growth in the MBE process to limit the evolution of the
level set function, and thus can avoid the re-initialization in the evolution
process and regulate the smoothness of the segmented curve. It also works for
noisy images with intensity inhomogeneity, which is a challenge in image
segmentation. To solve the variational model, we derive the gradient flow and
design scalar auxiliary variable (SAV) scheme coupled with fast Fourier
transform (FFT), which can significantly improve the computational efficiency
compared with the traditional semi-implicit and semi-explicit scheme. Numerical
experiments show that the proposed method can generate smooth segmentation
curves, retain fine segmentation targets and obtain robust segmentation results
of small objects. Compared to existing level set methods, this model is
state-of-the-art in both accuracy and efficiency
The Sensitivity of Simulated River Discharge to Land Surface Representation and Meteorological Forcings
Abstract
The discharge of freshwater into oceans represents a fundamental process in the global climate system, and this flux is taken into account in simulations with general circulation models (GCMs). Moreover, the availability of realistic river routing schemes is a powerful instrument to assess the validity of land surface components, which have been recognized to be crucial for the global climate simulation. In this study, surface and subsurface runoff generated by the 13 land surface schemes (LSSs) participating in the Second Global Soil Wetness Project (GSWP-2) are used as input fields for the Hydrology Discharge (HD) routing model to simulate discharge for 30 of the world's largest rivers. The simplest land surface models do not provide a good representation of runoff, and routed river flows using these inputs are affected by many biases. On the other hand, HD shows the best simulations when forced by two of the more sophisticated schemes. The multimodel ensemble GSWP-2 generates the best phasing of the annual cycle as well as a good representation of absolute values, although the ensemble mean tends to smooth the peaks. Finally, the intermodel comparison shows the limits and deficiencies of a velocity-constant routing model such as HD, particularly in the phase of mean annual discharge.
The second part of the study assesses the sensitivity of river discharge to the variation of external meteorological forcing. The Center for Ocean–Land–Atmosphere Studies version of the SSiB model is constrained with different meteorological fields and the resulting runoff is used as input for HD. River flow is most sensitive to precipitation variability, but changes in radiative forcing affect discharge as well, presumably because of the interaction with evaporation. Also, this analysis provides an estimate of the sensitivity of river discharge to precipitation variations. A few areas (e.g., central and eastern Asia, the Mediterranean, and much of the United States) show a magnified response of river discharge to a given percentage change in precipitation. Hence, an amplified effect of droughts as indicated by the consensus of climate change predictions may occur in places such as the Mediterranean. Conversely, increasing summer precipitation foreseen in places like southern and eastern Asia may amplify floods in these poor and heavily populated regions. Globally, a 1% fluctuation in precipitation forcing results in an average 2.3% change in discharge. These results can be used for the definition and assessment of new strategies for land use and water management in the near future
- …