We consider the global well-posedness of weak energy conservative solution to a general quasilinear wave equation through variational principle, where may form finite time cusp singularity, when concentrates. As main result in this paper, we construct Finsler type optimal transport metric, then prove that flow is Lipschitz under metric. also generic regularity by applying Thom's transversality ...

In this paper we present a general framework that allows one to study discretiza-tion of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent bundles respectively. In particular we show how to obtain a large class of discrete algorithms using this geometric approach. We give new geometric insight into t...

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...