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Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Variable Projection Methods for an Optimized Dynamic Mode Decomposition
A simple algorithm for computing an optimized version of the dynamic mode decomposition for data which may be collected at unevenly spaced sample times and finds that the resulting decomposition displays less bias in the presence of noise than standard DMD algorithms.
Multiresolution Dynamic Mode Decomposition
We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multiresolution analysis allows for a decomposition method capable of robustly separating complex…
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
The recent sparse identification of nonlinear dynamics (SINDY) modelling procedure is extended to include the effects of actuation and it is demonstrated that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes.
Deep learning in fluid dynamics
- J. Kutz
- Computer ScienceJournal of Fluid Mechanics
- 31 January 2017
Although neural networks have been applied previously to complex fluid flows, the article featured here is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows.
Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data
- J. Kutz
- Computer Science
- 15 September 2013
Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis, with emphasis on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences.
Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video
The DMD method is demonstrated to work robustly in real-time with personal laptop-class computing power and without any parameter tuning, which is a transformative improvement in performance that is ideal for video surveillance and recognition applications.
Flower discrimination by pollinators in a dynamic chemical environment
How hawkmoths sniff out a flower Pollinators such as butterflies and bees are the true targets of the flower odors we love so much. Though we might imagine insects “following their noses,” the wealth…
Low-dimensional functionality of complex network dynamics: neurosensory integration in the Caenorhabditis Elegans connectome.
- James M. Kunert, E. Shlizerman, J. Kutz
- BiologyPhysical review. E, Statistical, nonlinear, and…
- 24 October 2013
The first full dynamic model of the neural voltage excitations that allows for a characterization of network structures which link input stimuli to neural proxies of behavioral responses is posit, showing that robust, low-dimensional bifurcation structures drive neural voltage activity modes.
A Unified Framework for Sparse Relaxed Regularized Regression: SR3
The advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, and greater flexibility) are demonstrated across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity.