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 #AI #Koopmanoperator #ML #dynamicalsystems #chaostheory

RT @wredman4: 🚨 new paper out in Chaos "Koopman Learning with Episodic Memory"! Really excited about this work and,…

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 conditions, and thus lack of predictability despite the simplicity of its description. We only saw the proof of its "chaoticity" in 2004 But the attractor still holds secrets. For example, with #Koopmantheory we discovered complex-valued observables that have much better #predictability and less sensitivity to initial conditions than typical for this system. One of those observables - discovered first by spectral projection method in - whose contour plot from the paper is shown below as a) - looks like a sinusoid on a Mobius strip. It was found with a different method in . The b) figure below - from that paper - shows the plot of the evolution of the "regular" observable compared with the sinusoid, to indicate its regularity. In contrast, part c) shows the typical chaotic evolution of time series of observables on the Lorenz attractor.

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 (KAN's) are theoretically interesting and offer computational advantages in this context. Here is an interesting paper utilizing these structures #AI #ML #KoopmanOperator @Aimdyn_Inc

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

RT @wredman4: Our paper "Identifying Equivalent Training Dynamics" was accepted as a spotlight (top ~5%) 💡 to NeurIPS! A real dream team (b…

RT @wredman4: A big thanks to the great team!: @hopfbifurcator @s_acosta_4 @ninamiolane Newest version of the paper:

@RossDynamicsLab Word!

Nice recognition by the USA Today that #Koopmanoperator based AI systems provide a framework for real time diagnostics and reasoning for network security threats! Congrats to everyone at @MixModeAI ! #AI #ML

AI omnipresent these days but most of the news we hear are about LLM's and generative AI for visuals. There is much more use for #AI , some in areas such as human ability improvement. Here is one that can be applied to rehabilitation from hand injuries #KoopmanOperator #ML

USA News and World report issued their latest rankings . It is interesting that UCSB, is 6th (!!!!) in the nation measuring Faculty Research Impact (second of all public schools)! By my count in front of it are only MIT, Stanford, Harvard, Berkeley and Princeton...

For Koopman modelers: I added to my Youtube channel the series of videos on the PyKMD software. #AI #KoopmanOperator #ML #DynamicalSystems

The need for a paradigm shift in building AI models is clear. #AI #Koopman #ML

My July lecture at the Fields Institute on "The Operator is the Model" is at #AI #ML #dynamicalsystems #KoopmanOperator #theoperatoristhemodel

Given my training in guitar, I feel there is a full circle achieved with this paper that considers dynamics of strings of musical instruments using Koopman operator-based machine learning 😀. Added bonus: comps to a number of other methods, all outperformed by the Koopman spectral method. #dynamicalsystems #theoperatoristhemodel #AI #ML #Koopmanoperator

One of the reasons AI systems need an enormous amount of training and associated energy is that they do not feature a layered design that separates perception (detection), reasoning and communication. @MixModeAI 's AI -featuring @Aimdyn_Inc's Koopman operator based methodology for network security - features such design, enabling it to train lean, personalized, real-time adaptive AI models on customers networks. #AI #ML #leanAI #KoopmanOperator #DynamicalSystems

@ylecun @ylecun I fully agree. MPC for nonlinear models where non-convexity can be a factor can be convexified as in BTW it does not have to be MPC, sometimes LQR suffices: #AI #ML #OptimalControl #Koopman #DynamicalSystems

I found it interesting that the "quadratic" (or "square root") nature of QM probabilities actually has a classical correspondence in dynamical systems theory , see Remark 2 in This renders the Bohr interpretation as natural if one insists on computing classical probabilities via unitary operators. #quantumphysics