Variational principles for multisymplectic second-order classical field theories

Variational Methods for Field Theories

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*................... 1 GENERAL INTRODUCTION ~.~O................................*............ 3 Part I: Confinement in Periodic Quantum Electrodynamics for Low Couplings

Classical Field Theory on Lie Algebroids: Multisymplectic Formalism

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a Lagrangian function is given, we find the equations of motion in terms of a Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism is als...

Second-order algebraic theories

Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the vie...

Second-order stochastic variational inference

Stochastic gradient descent (SGD), the workhorse of stochastic optimization, is slow in theory (sub-linear convergence) and in practice (thousands of iterations), intuitively for two reasons: 1) Its learning rate schedule is fixed a priori and decays rapidly enough to 0 that is square-summable. This learning rate schedule limits the step size and hence the rate of convergence for a Lipschitz ob...

Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities