Publications (8)
The remapped particle-mesh advection scheme
Colin J. Cotter, Jason Frank, Sebastian Reich
We describe the remapped particle-mesh method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compre…
Projected Shadowing-based Data Assimilation
Bart de Leeuw, Svetlana Dubinkina, Jason Frank +3
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refin…
Symplectic Runge-Kutta discretization of a regularized forward-backward sweep iteration for optimal control problems
Xin Liu, Jason Frank
Li, Chen, Tai & E. (J. Machine Learning Research, 2018) have proposed a regularization of the forward-backward sweep iteration for solving the Pontryagin maximum principle in optim…
A detectability criterion and data assimilation for non-linear differential equations
Jason Frank, Sergiy Zhuk
In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapu…
Least-biased correction of extended dynamical systems using observational data
Keith Myerscough, Jason Frank, Benedict Leimkuhler
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints…
Direct control of the small-scale energy balance in 2D fluid dynamics
Jason Frank, Benedict Leimkuhler, Keith Myerscough
We explore the direct modification of the pseudo-spectral truncation of 2D, incompressible fluid dynamics to maintain a prescribed kinetic energy spectrum. The method provides a me…
Exponentially convergent data assimilation algorithm for Navier-Stokes equations
Jason Frank, Tigran Tchrakian, Sergiy Zhuk
The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in…
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism
Swinda K. J. Falkena, Courtney Quinn, Jan Sieber +2
Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as th…