MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flows

The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the fact that many variants of GANs were developed following this paradigm, the current theoretical understanding of GANs and their practical algorithms are inconsistent. In this paper, we leverage Wasserstein gradient flows which characterize the evolution of particles in the sample space, to gain theoretical insights and algorithmic inspiration of GANs. We introduce a unified generative modeling framework - MonoFlow: the particle evolution is rescaled via a monotonically increasing mapping of the log density ratio. Under our framework, adversarial training can be viewed as a procedure first obtaining MonoFlow's vector field via training the discriminator and the generator learns to draw the particle flow defined by the corresponding vector field. We also reveal the fundamental difference between variational divergence minimization and adversarial training. This analysis helps us to identify what types of generator loss functions can lead to the successful training of GANs and suggest that GANs may have more loss designs beyond the literature (e.g., non-saturated loss), as long as they realize MonoFlow. Consistent empirical studies are included to validate the effectiveness of our framework

MonoFlow:Rethinking Divergence GANs via the Perspective of Differential Equations

The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the fact that many variants of GANs were developed following this paradigm, the current theoretical understanding of GANs and their practical algorithms are inconsistent. In this paper, we leverage Wasserstein gradient flows which characterize the evolution of particles in the sample space, to gain theoretical insights and algorithmic inspiration of GANs. We introduce a unified generative modeling framework – MonoFlow: the particle evolution is rescaled via a monotonically increasing mapping of the log density ratio. Under our framework, adversarial training can be viewed as a procedure first obtaining MonoFlow’s vector field via training the discriminator and the generator learns to draw the particle flow defined by the corresponding vector field. We also reveal the fundamental difference between variational divergence minimization and adversarial training. This analysis helps us to identify what types of generator loss functions can lead to the successful training of GANs and suggest that GANs may have more loss designs beyond the literature (e.g., non-saturated loss), as long as they realize MonoFlow. Consistent empirical studies are included to validate the effectiveness of our framework.<br/

Pseudo-peakons and Cauchy analysis for an integrable fifth-order equation of Camassa-Holm type

In this paper we discuss integrable higher order equations {\em of Camassa-Holm (CH) type}. Our higher order CH-type equations are "geometrically integrable", that is, they describe one-parametric families of pseudo-spherical surfaces, in a sense explained in Section 1, and they are integrable in the sense of zero curvature formulation ($\simeq$ Lax pair) with infinitely many local conservation laws. The major focus of the present paper is on a specific fifth order CH-type equation admitting {\em pseudo-peakons} solutions, that is, weak bounded solutions with differentiable first derivative and continuous and bounded second derivative, but such that any higher order derivative blows up. Furthermore, we investigate the Cauchy problem of this fifth order CH-type equation on the real line and prove local well-posedness under the initial conditions $u_0 \in H^s(\mathbb{R})$, $s > 7/2$. In addition, we study conditions for global well-posedness in $H^4(\mathbb{R})$ as well as conditions causing local solutions to blow up in a finite time. We conclude our paper with some comments on the geometric content of the high order CH-type equations.Comment: 6 figures; 32 page

Analytical Properties for the Fifth Order Camassa-Holm (FOCH) Model

This paper devotes to present analysiswork on the fifth order Camassa-Holm (FOCH) modelwhich recently proposed by Liu and Qiao. Firstly, we establish the local and global existence of the solution to the FOCH model. Secondly, we study the property of the infinite propagation speed. Finally, we discuss the long time behavior of the support of momentum density with a compactly supported initial data

Application of implicit pressure-explicit saturation method to predict filtrated mud saturation impact on the hydrocarbon reservoirs formation damage

Hydrocarbon reservoirs&rsquo; formation damage is one of the essential issues in petroleum industries that is caused by drilling and production operations and completion procedures. Ineffective implementation of drilling fluid during the drilling operations led to large volumes of filtrated mud penetrating into the reservoir formation. Therefore, pore throats and spaces would be filled, and hydrocarbon mobilization reduced due to the porosity and permeability reduction. In this paper, a developed model was proposed to predict the filtrated mud saturation impact on the formation damage. First, the physics of the fluids were examined, and the governing equations were defined by the combination of general mass transfer equations. The drilling mud penetration in the core on the one direction and the removal of oil from the core, in the other direction, requires the simultaneous dissolution of water and oil flow. As both fluids enter and exit from the same core, it is necessary to derive the equations of drilling mud and oil flow in a one-dimensional process. Finally, due to the complexity of mass balance and fluid flow equations in porous media, the implicit pressure-explicit saturation method was used to solve the equations simultaneously. Four crucial parameters of oil viscosity, water saturation, permeability, and porosity were sensitivity-analyzed in this model to predict the filtrated mud saturation. According to the results of the sensitivity analysis for the crucial parameters, at a lower porosity (porosity = 0.2), permeability (permeability = 2 mD), and water saturation (saturation = 0.1), the filtrated mud saturation had decreased. This resulted in the lower capillary forces, which were induced to penetrate the drilling fluid to the formation. Therefore, formation damage reduced at lower porosity, permeability and water saturation. Furthermore, at higher oil viscosities, due to the increased mobilization of oil through the porous media, filtrated mud saturation penetration through the core length would be increased slightly. Consequently, at the oil viscosity of 3 cP, the decrease rate of filtrated mud saturation is slower than other oil viscosities which indicated increased invasion of filtrated mud into the formation

Rogue peakon, well-posedness, ill-posedness and blow-up phenomenon for an integrable Camassa-Holm type equation

In this paper, we study an integrable Camassa-Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution - called {\sf rogue peakon}, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space $B_{p,r}^{s}$ with $1\leq p,r\leq\infty$, $s>\max \left\{1+1/p,3/2\right\}$ or $B_{2,1}^{3/2}$, and then prove the ill-posedness of the solution in $B_{2,\infty}^{3/2}$. Moreover, we establish the global existence and blow-up phenomenon of the solution, which is, if $m_0(x)=u_0-u_{0xx}\geq(\not\equiv) 0$, then the corresponding solution exists globally, meanwhile, if $m_0(x)\leq(\not\equiv) 0$, then the corresponding solution blows up in a finite time.Comment: 23 pages, 6 figure

Beyond Triplet: Leveraging the Most Data for Multimodal Machine Translation

Multimodal machine translation (MMT) aims to improve translation quality by incorporating information from other modalities, such as vision. Previous MMT systems mainly focus on better access and use of visual information and tend to validate their methods on image-related datasets. These studies face two challenges. First, they can only utilize triple data (bilingual texts with images), which is scarce; second, current benchmarks are relatively restricted and do not correspond to realistic scenarios. Therefore, this paper correspondingly establishes new methods and new datasets for MMT. First, we propose a framework 2/3-Triplet with two new approaches to enhance MMT by utilizing large-scale non-triple data: monolingual image-text data and parallel text-only data. Second, we construct an English-Chinese {e}-commercial {m}ulti{m}odal {t}ranslation dataset (including training and testing), named EMMT, where its test set is carefully selected as some words are ambiguous and shall be translated mistakenly without the help of images. Experiments show that our method is more suitable for real-world scenarios and can significantly improve translation performance by using more non-triple data. In addition, our model also rivals various SOTA models in conventional multimodal translation benchmarks.Comment: 8 pages, ACL 2023 Findin

Research on the Creative Application of Origami Performance Techniques in Clothing

Origami has various manifestations and rich production techniques, and it is regarded as one of the indispensable contemporary art forms. In order to enrich the creative expressions of fashion design, this paper summarises the creative application forms of origami art in fashion design from the external and moulding characteristics of origami, studies the fabric characteristics through experimental verification, and summarises the applicable techniques of expression. The results show that the folding application forms of origami art and clothing modelling can be realised by using the expression methods of ironing and crimping, stitching texture moulding and repeated combination moulding, that is, pattern deformation folding application, fabric transformation folding application and modular combination folding application. The application of the folding form in clothing three-dimensional modelling and surface texture can give full play to the unique modelling beauty and artistic style of origami art and provide a reference for creative ideas in clothing design

On the Cauchy Problem for the b

In this paper, we consider b-family equations with a strong dispersive term. First, we present a criterion on blow-up. Then global existence and persistence property of the solution are also established. Finally, we discuss infinite propagation speed of this equation