The variational principle of barotropic Eulerian fluid dynamics is known to be quite cumbersome containing as much as eleven independent functions. This is much more than the the four functions (density and velocity) appearing in the Eulerian equations of motion. This fact may have discouraged applications of the variational method. In this paper a four function Eulerian variational principle i...

We establish the variational principle of Kolmogorov-PetrovskyPiskunov (KPP) front speeds in a one dimensional random drift which is a mean zero stationary ergodic process with mixing property and local Lipschitz continuity. To prove the variational principle, we use the path integral representation of solutions, hitting time and large deviation estimates of the associated stochastic flows. The...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

As we will see during this talk, the Bayesian and information-theoretic views of variational inference provide complementary and mutually beneficial perspectives to the same problems with two different languages. More specifically, based on the paper by Honkela and Valpola [4], we will provide an interpretation of variational inference based on the MDL principle as a theoretical framework for m...

We introduce a variational principle suitable for the computational modeling of crystalline materials. We consider a class of materials that are described by non-quasiconvex variational integrals. We are further focused on equlibria of such materials that have non-attainment structure, i.e., Dirichlet boundary conditions prohibit these variational integrals from attaining their infima. Conseque...