There is more than one way to extend operator theoretic approach to dynamical systems to systems with input (control systems). One is to extend the state space to include sequences of control inputs, as in https://t.co/gh2R3AqjHA , another deals with families of Koopman operators

This week, University of California set a record with winning wins 5 Nobel Prizes in 3 days. 2 of these went to UCSB. I asked ChatGPT to give me the list of Universities with the highest number of Nobel prizes in the last 30 years. Here is what it came up with. 😃 #Nobel #UCSB

Wow. 2 Nobel prizes to UCSB today, and all 3 to University of California https://t.co/fpYzpYodUu! 2 Nobels to the same institution in one year is a somewhat rare event. Congratulations to Prof. Clarke, Devoret and Martinis! Last time this happened at UCSB was 2000. Note: some

On static Koopman operators: every ML approach, including transformers, at the final step represents output (y) as a sum of (possibly nonlinear) functions of input (x) i.e. lifting of x. In https://t.co/xZry4xBc9h I introduced the notion of linear operators associated with maps

On static Koopman operators: every ML approach, including transformers, at the final step represents output (y) as a sum of (possibly nonlinear) functions of input (x) i.e. lifting of x. In https://t.co/ArORa59JUB I introduced the notion of linear operators associated with maps

My talk at the Koopman Operator Theory II Workshop is here https://t.co/9vaJL8h8t2 In it, 2 new topics are discussed: functional spaces for control systems (with Jorge Cortes and Masih Haseli) and the notion of static Koopman (composition, pullback) operators for mappings between

For all Koopmanistas, the talks from the KOT II conference are now online! Thanks to @ErvinKamenar for the organization and Marko Kozlov for his excellent work on the recordings. You can find all the talks on the YouTube Playlist: https://t.co/kFg1tqaiKt #KoopmaOperator

As I mentioned in another post, the advances in Koopman Operator theory and applications are happening at a fast pace, especially in AI and control applications. At the meeting, https://t.co/oEWgBuMzi7 expertly organized by Ervin Kamenar we expect a vigorous discussion that will

The use of Koopman operator theory in control is advancing at a fast pace. Here is a survey of theoretical guarantees that establish the backbone for computations and applications https://t.co/XhpXyqSNJo. #Koopmanoperator #controltheory #AI #ML

Survey article: "An overview of Koopman-based control: From error bounds to closed-loop guarantees" (by Robin Strässer, Karl Worthmann, Igor Mezić, Julian Berberich, Manuel Schaller, Frank Allgöwer):

Foundational models collect all the data from all available instances of the process (e.g. language) to parametrize input to output relationships - interpolatively, with no real time updates. In contrast, the human brain collects data individualized to the process from relatively

This paper applying Koopman to badger movement is fun, especially given my postdoc was in math biology at @warwickuni (loved it there!), https://t.co/qGcY3owKh6

A nice application of #Koopmanoperator theory to galactic dynamics here:

Last May, we held a workshop in Otranto, Italy, connecting Koopman operator theory and climate science. Here is a writeup on it https://t.co/RYwEyvjkLy #AI #Koopmanoperator #ML #dynamicalsystems #chaostheory

🚨 new paper out in Chaos "Koopman Learning with Episodic Memory"! https://t.co/nQ2hYfd02y Really excited about this work and, as always, a real honor to work with @IgorMezic and @Aimdyn_Inc 1/10

I got into science in no small part due to reading James Gleick's "#Chaos" with its wonderful depictions of the discovery process. #Lorenzattractor was one of those great discoveries. It is an example of a physical system exhibiting chaotic motion and sensitivity to initial

AI for dynamical systems: the architecture that incorporates 1) a block of DNN for embeddings (feature engineering) and 2) a block of Koopman Operator based predictor/controller is emerging as a promising one in terms of accuracy and lean computation. Kolmogorov Arnold Networks

Koopman Operator Theory provides a framework for #metalearning of #neuralnetworks . Our paper https://t.co/LuBZjNkwLg - accepted as #NeurIPS highlight - with @wredman4 et al. provides methodology for comparing neural network training protocols. #AI #ML #KoopmanOperator