Models of neural machine translation are often from a discriminative family of encoder-decoders that learn a conditional distribution of a target sentence given a source sentence. In this paper, we propose a variational model to learn this conditional distribution for neural machine translation: a variational encoder-decoder model that can be trained end-to-end. Different from the vanilla encod...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

Many real-valued stochastic time-series are locally linear (Gaussian), but globally nonlinear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. We present a mixed-state dynamic graphical model in which a hidden Markov model drives a linear dynamic system. This combination allows us t...

We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter ε > 0. Smaller ε leads to finer ramification patterns, and we analyse how optimal network patterns in a particular geometry behave as ε → 0 by proving an energy scaling law. This entails providing...

We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle tech...

One of the main technique used to recover motion analysis from two images or to register them is variational optical flow, where the pixels of one image are matched to the pixels of the second image by minimizing an energy functional. In the standard formulation of variational optical flow, the estimated motion vector field depends on the reference image and is asymmetric. However, in most appl...

We present a novel variational approach to image restoration (e.g., denoising, inpainting, labeling) that enables us to complement established variational approaches with a histogram-based prior, enforcing closeness of the solution to some given empirical measure. By minimizing a single objective function, the approach utilizes simultaneously two quite different sources of information for resto...

Deterministic evolutions, generated by dissipative operators in Banach spaces, can be characterized using a set of integral inequalities. Such characterization is particularly useful in the nonlinear context. In this paper, we exploit such technique for variational problems appearing in the rate function of large deviation of innnite dimensional processes. We extend the method of rate function ...