We study general mathematical framework for variation of potential energy with respect to domain deformation. It enables rigorous derivation of the integral formulas for the energy release rate in crack problems. Applying a technique of the shape sensitivity analysis, we formulate the shape derivative of potential energy as a variational problem with a parameter. Key tools of our abstract theor...

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a varia...

Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the inference model. We introduce Adversarial Variational Bayes (AVB), a technique for training Variational Autoencoders with arbitrarily expressive inference mo...

Sensitivity analysis of solution for variational inequalities and variational inclusions has been studied by many authors via quite different technique. See 1–7 and the reference therein . In 2004, Agarwal et al. 1 introduced and studied the following problem which is called the system of parametric generalized nonlinear mixed quasi variational inclusions. Let H be a real Hilbert space endowed ...

Co-clustering has emerged as an important technique for mining contingency data matrices. However, almost all existing coclustering algorithms are hard partitioning, assigning each row and column of the data matrix to one cluster. Recently a Bayesian co-clustering approach has been proposed which allows a probability distribution membership in row and column clusters. The approach uses variatio...

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

In this paper, we propose a novel statistical decap allocation method to reduce the voltage drop noise in the presence of variational leakage current sources. The new method can derive the closed form of decoupling capacitance (decaps) in terms of variational parameters from the variational leakage currents. It treats the deterministic decap method as a black box and can work with any existing ...

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference [20, 4] has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theo...

Bending, buckling and vibration behaviors of nonlocal Timoshenko beams are investigated in this research using a variational approach. At first, the governing equations of the nonlocal Timoshenko beams are obtained, and then the weak form of these equations is outlined in this paper. The Ritz technique is selected to investigate the behavior of nonlocal beams with arbitrary boundary conditions ...