This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a
stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models,
we present a general framework for introducing stochasticity into variational principles …

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …

In recent works, beginning with [76], several stochastic geophysical fluid dynamics (SGFD)
models have been derived from variational principles. In this paper, we introduce a new …

Classical geometric mechanics, including the study of symmetries, Lagrangian and
Hamiltonian mechanics, and the Hamilton–Jacobi theory, are founded on geometric …

Smooth solutions of the incompressible Euler equations are characterized by the property
that circulation around material loops is conserved. This is the Kelvin theorem. Likewise …

We extend the Itô–Wentzell formula for the evolution of a time-dependent stochastic field
along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Itô …

We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating
noise and dissipation into mechanical systems arising from the theory of reduction by …

With the emergence of deep learning methods, new computational frameworks have been
developed that mix symbolic expressions with efficient numerical computations. In this work …