43 citations · 72 across the 6 of their papers we have counts for
8 papers
A Tutorial on Bayesian Data Assimilation
Colin Grudzien, Marc Bocquet
This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies…
Data assimilation for chaotic dynamics
Alberto Carrassi, Marc Bocquet, Jonathan Demaeyer +3
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Da…
Asymptotic forecast uncertainty and the unstable subspace in the presence of additive model error
Colin Grudzien, Alberto Carrassi, Marc Bocquet
It is well understood that dynamic instability is among the primary drivers of forecast uncertainty in chaotic, physical systems. Data assimilation techniques have been designed to…
Structure- & Physics- Preserving Reductions of Power Grid Models
Colin Grudzien, Deepjyoti Deka, Michael Chertkov +1
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies…
Degenerate Kalman filter error covariances and their convergence onto the unstable subspace
Marc Bocquet, Karthik S. Gurumoorthy, Amit Apte +3
The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and co-aut…
The Instability of the Hocking-Stewartson Pulse and its Geometric Phase in the Hopf Bundle
Colin Grudzien
This work demonstrates an innovative numerical method for counting and locating eigenvalues with the Evans function. Utilizing the geometric phase in the Hopf bundle, the technique…
Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution
Karthik S. Gurumoorthy, Colin Grudzien, Amit Apte +2
We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the…
Finding Eigenvalues the Rupert Way
Colin J. Grudzien, Tom J. Bridges, Christopher K. R. T. Jones
We develop a stability index for the travelling waves of non-linear reaction diffusion equations using the geometric phase induced on the Hopf bundle $S^{2n-1} \subset \mathbb{C}^n…