699 citations · 1.2k across the 12 of their papers we have counts for
12 papers
Projected Data Assimilation using Sliding Window Proper Orthogonal Decomposition
Aishah Albarakati, Marko Budisic, Erik Van Vleck
Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model.…
Modern Koopman Theory for Dynamical Systems
Steven L. Brunton, Marko Budišić, Eurika Kaiser +1
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymp…
Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
Aishah Albarakati, Marko Budišić, Rose Crocker +6
The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques…
Using braids to quantify interface growth and coherence in a rotor-oscillator flow
Margaux Filippi, Marko Budisic, Michael R. Allshouse +3
The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such…
Mesochronic classification of trajectories in incompressible 3D vector fields over finite times
Marko Budišić, Stefan Siegmund, Doan Thai Son +1
The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we clas…
Finite-Time Braiding Exponents
Marko Budisic, Jean-Luc Thiffeault
Topological entropy is a common measure of the rate of mixing in a flow. It can be computed by partition methods, or by estimating the growth rate of material lines or other materi…
Conditioning moments of singular measures for entropy maximization II: Numerical examples
Marko Budišić, Mihai Putinar
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous…
Braidlab: A Software Package for Braids and Loops
Jean-Luc Thiffeault, Marko Budisic
Braidlab is a Matlab package for analyzing data using braids. It was designed to be fast, so it can be used on relatively large problems. It uses the object-oriented features of Ma…
Frontiers of chaotic advection
Hassan Aref, John R. Blake, Marko Budišić +20
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid…
Applied Koopmanism
Marko Budišić, Ryan M. Mohr, Igor Mezić
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincaré's geometric picture that focuses on "dynamics of states". While this p…
Geometry of the ergodic quotient reveals coherent structures in flows
Marko Budišić, Igor Mezić
Dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach. However, by identifying coherent structures in their state spaces, i.e…
Conditioning moments of singular measures for entropy optimization. I
Marko Budišić, Mihai Putinar
In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue…