Karthik Elamvazhuthi

YouTube video by Automatic Control Engineering Network (ACE) ACE AI and Data Talk Series-Dr. Karthik Elamvazhuthi

Finally, my YouTube debut! A recording of my talk at the AI and data seminar series organized by the Automatic Control Engineering Network.
m.youtube.com/watch?v=o-4B...

Here I pontificate on using time reversals of diffusions for stabilization and planning problems.

I am starting to compile some notes on Generative Modeling for Control Theory. The goal is to include topics such as degenerate Fokker-Planck equations (FPEs) and Optimal transport theory. Here is a first post on the classical (nicer) FPE and its long-term behavior.

hackmd.io/@clopenloop/...

That’s an amazing stat 😵

Fun tangential fact: The idea of velocity-averaging in the flow matching can be found in Lacker's notes on mean-field control. He refers to it as "mimicking".

Probably a good chapter if it starts with Nietzsche.

- Tanja Eisner, Bálint Farkas, Markus Haase and
Rainer Nagel (Operator Theoretic Aspects
of Ergodic Theory)

I like how some inequalities were derived for fun. 😄

Universal Approximation of Mean-Field Models via Transformers This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomen...

Permutation equivariance is a common property of multi-agent systems. In a new paper with Shiba Biswal and
@rishisonthalia.bsky.social
‬, accepted to ICML, we leverage this property shared by transformers, for mean field models of collective behavior.

#machinelearning

arxiv.org/abs/2410.16295

From Combinatorics to Partial Differential Equations The optimal matching of point clouds in $\mathbb{R}^d$ is a combinatorial problem; applications in statistics motivate to consider random point clouds, like the Poisson point process. There is a cruci...

Nice set of notes connecting the finite particle matching problem to the continuum optimal transport solution.

arxiv.org/abs/2505.10175

Analysis of Heat Equations on Domains. (LMS-31)

A reference for Markov semigroups that I have found extremely useful.
press.princeton.edu/books/hardco...

People are talking about controls in Bluesky?! Where?

Nice timeline! Adjoint equations arose in optimal control of finite dimensional ODE systems initially due to Pontryagin and coworkers extending methods of calculus of variations. Lions popularized them for infinite dimensional systems like PDEs.

It’s known that the Laplacian operator, describing how heat flows through a domain, carries rich information about the domain’s underlying geometry. Similarly, one can understand the geometry of a control system using its sub-Laplacian.

See

comptes-rendus.academie-sciences.fr/mathematique...

🎙️ New episode! Anders Rantzer (@lunduniversity) walks us through robust control, IQCs, the KYP lemma, nonlinear and hybrid systems, scalability and positivity, and dual (adaptive) control. A journey shaped by the dialogue between Western and Russian control traditions — don’t miss it! 🧠🚀

Optimal Trajectories and the Neoclassical Calculus of Variations - Set-Valued and Variational Analysis The calculus of variations, a venerable subject connected for centuries with physics, was largely superseded in the 1960s by the theory of optimal control that arose then from modern engineering. Math...

Nice survey on the how optimal control needed some genuine innovations over classical calculus of variation, and how non-smooth tools apply in this setting.

No mention of needle variations, unfortunately.

link.springer.com/article/10.1...

If we are not careful, all our jobs will be replaced by conditional probability distributions.

Denoising an unstable double integrator to sum of two Dirac measures.

See details on the theory in the preprint: www.researchgate.net/publication/...

#controltheory #machinelearning #diffusionmodels

bsky.app/profile/clop...

A blog post on how diffusion models can be used for planning in domains with obstacles : hackmd.io/@TAzH1D5uSQO...

When it comes to optimal transport, think Eulerian and compute Lagrangian. In a new paper, we present a numerical method embracing this philosophy, with potential applications to controlling swarms and sampling.

www.esaim-cocv.org/articles/coc...

Optimal transport of linear systems over equilibrium measures We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and ta…

Why did the robot swarm cross the road? Because, it wasn’t at equilibrium. 🤖 🤖

In a new paper, we prove existence of optimal transport maps between singular measures called equilibrium measures, when the flow is constrained to be a linear control system.

www.sciencedirect.com/science/arti...

In case you are interested in alternatives for Google scholar, base seems like a nice option: www.base-search.net

Gender and retention patterns among U.S. faculty Women faculty are more likely to leave their jobs than men, most often due to workplace climate, rather than work-life balance.

Women leave academia at higher rates than men at every career stage, and attrition is especially high among three groups: tenured faculty, women in non-STEM fields, and women employed at less prestigious institutions, a #ScienceAdvances analysis finds.

Convexity lies in the eye of beholder. A note on how nonlinear optimal control problems can be given a convex formulation using the continuity equation. hackmd.io/@TAzH1D5uSQO... #controltheory

Switching between two flows of a skinny neural ODE (blue and red) produces the behavior of a time-averaged thick neural ODE (green).

The Averaging Theory Behind Narrow Neural ODEs - HackMD

Averaging theory in dynamical systems has found interesting applications from stable inverted pendulums to undulating snakes and flapping wings of humming birds. Turns out there is also a lot of averaging theory behind approximation properties of neural networks. A note: hackmd.io/hkIgH3ZJRjyu...

If you are looking for fun in G'ville, here is your chance! Also, to my colleagues, let me know if you have suggestions for tweaks in content.

Simons Institute for the Theory of Computing and SLMath Joint Workshop: AI for Mathematics and Theoretical Computer Science This is an exciting time for mathematics, as new technologies for mathematical reasoning provide novel opportunities for mathematical research, communication, and discovery. Mathlib, a library of form...

*AI for Mathematics and Theoretical Computer Science*, a workshop hosted jointly by the Simons Institute for the Theory of Computing and the Simons Laufer Mathematical Sciences Institute, will be held in Berkeley at April 7-11, 2025.

simons.berkeley.edu/workshops/si...

Collective decision making leads to some unusual control problems, that are problably the most relevant from a distributed intelligence point of view. A musing about a toy model on honey bey site selection:
hackmd.io/@TAzH1D5uSQO...

Link to slides on a talk I gave at UCSB’s math department on extending score matching based generative modeling for control problems.

drive.google.com/file/d/1IZOS...

Denoising Diffusion-Based Control of Nonlinear Systems We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that have achieved success...

Anyone in the control theory community going to IEEE CDC willing to help us out to present a paper for us? Me and our collaborators are having visa issues.

I will provide the slides. The work is at the intersection of diffusion based generative modeling and control theory: arxiv.org/abs/2402.02297

Identification of Mean-Field Dynamics using Transformers This paper investigates the use of transformer architectures to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in mode...

An interesting property of transformers is their permutation invariance. This makes them particularly suitable for modeling large interacting particle systems and multi-agent agent phenomena.

Joint work with Shiba Biswal (LANL) and Rishi Sonthalia (BC)

arxiv.org/abs/2410.16295