variational's Usage Examples:

equations structurally identical to the Einstein field equations are derivable from a variational principle.

In statistics, the evidence lower bound (ELBO, also variational lower bound or negative variational free energy) is a quantity which is often optimized.

By invoking the variational method, one can derive a set of N-coupled equations for the N spin orbitals.

In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a Functional.

In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states.

ONETEP therefore combines the advantages of the plane-wave approach (controllable accuracy and variational convergence of the total energy with respect.

The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus.

in deep learning and computer vision, specifically in the context of variational autoencoders, for modeling the pixel intensities of natural images.

\end{align}Alternate proofThe Hellmann–Feynman theorem is actually a direct, and to some extent trivial, consequence of the variational principle (the Rayleigh-Ritz variational principle) from which the Schrödinger equation may be derived.

Charles Keil classified forms and formal detail as "sectional, developmental, or variational.

variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding such functions which optimize the values.

A more recent and definitive graphics refinement (1980s) is minimax eversions, which is a variational method, and consist of special homotopies (they.

Notable example of where the Hellmann–Feynman is not applicable is for example finite-order Møller–Plesset perturbation theory, which is not variational.