41 citations · 115 across the 7 of their papers we have counts for
8 papers
Meta-Learning Fourier Neural Operators for Hessian Inversion and Enhanced Variational Data Assimilation
Hamidreza Moazzami, Asma Jamali, Nicholas Kevlahan +1
Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions…
Second order adjoint sensitivity analysis in variational data assimilation for tsunami models
N. K. -R. Kevlahan, R. A. Khan
We mathematically derive the sensitivity of data assimilation results for tsunami modelling, to perturbations in the observation operator. We consider results of variational data a…
Convergence analysis of a variational data assimilation scheme for bathymetry detection from surface wave observations
N. K. -R. Kevlahan, R. A. Khan
Accurate mapping of ocean bathymetry is a multi-faceted process, needed for safe and efficient navigation on shipping routes and for predicting tsunami waves. Currently available b…
On the convergence of data assimilation for the one-dimensional shallow water equations with sparse observations
N. K. -R. Kevlahan, R. Khan, B. Protas
The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. We consider the problem of optimally determining the initial condition…
Compressive sampling for energy spectrum estimation of turbulent flows
Gudmundur F. Adalsteinsson, Nicholas K. -R. Kevlahan
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyqu…
A conservative adaptive wavelet method for the shallow water equations on the sphere
Matthias Aechtner, Nicholas Kevlahan, Thomas Dubos
We introduce an innovative wavelet-based approach to dynamically adjust the local grid resolution to maintain a uniform specified error tolerance. Extending the work of Dubos and K…
Shock interactions, turbulence, and the origin of the stellar mass spectrum
Ralph E. Pudritz, N. K. -R. Kevlahan
Supersonic turbulence is an essential element in understanding how structure within interstellar gas is created and shaped. In the context of star formation, many computational stu…
Shock generated vorticity in the interstellar medium and the origin of the stellar initial mass function
N. Kevlahan, Ralph E. Pudritz
The main observational evidence for turbulence in the interstellar medium (ISM) and molecular clouds is the power-law energy spectrum for velocity fluctuations, E(k) \propto k^α. T…