Applications of the calculus of variations include:
Variational method (quantum mechanics), one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states;
Variational Bayesian methods, a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.
Variational methods in general relativity, a family of techniques using calculus of variations to solve problems in Einstein's theory of general relativity.
Finite element method is a variational method for finding approximate solutions to boundary value problems in differential equations.
