HydroGym: A Reinforcement Learning Platform for Fluid Dynamics Now published in Nature!! nature.com/articles/s41586-0… GitHub: github.com/dynamicslab/hydro… Amazing collaboration with Christian Lagemann, S Mokbel, M Gondrum, M Rüttgers, Y Wang, P Suárez, L Paehler, D A Bezgin, A B Buhendwa, J L Callaham, S Ahnert, N Zolman, X Shao, J-Ch Loiseau, N A. Adams, M Meinke, W Schröder, K Lagemann, E Lagemann, R Vinuesa & S L Brunton

The Navier-Stokes equations are among the most important — and most challenging — equations in physics. So, what makes them so difficult? And how could a new OpenAI proof finally resolve the problem? Watch our new video: piped.video/watch?v=PsWR1rQE…

Very nice video by @MichiganAero highlighting the research in the VinuesaLab! Thanks to everyone in my group as well for your excellent work! More on understanding and control turbulent flows and on generative AI for aerodynamic design and optimization!! piped.video/watch?v=cbamiovW…

Very cool benchmark environment for robot learning!! The NSF AI Institute in Dynamic Systems is optimistically developing benchmark environments for learning across the engineering and natural sciences -- try this one out!!

GPT-6 Astra is impressive, but agentic robotics ≠ just control. Physical agents should control robots, learn new skills, and design their own hardware. So we introduce RLE-Bench: 48 everyday robotics engineering tasks spanning closed-loop control, policy learning, perception, and mechanical design.

New post: quantifying Gauss-Seidel's loop-carried dependency with OSACA, and a loop-unrolling fix that cuts it from 12 to 2 cycles/element. Three compiler experiments included to isolate the effect from vectorization. 👉 tinyurl.com/3h79t8fn

With all the Navier–Stokes excitement, I almost forgot to say that our tiny billiard ball has made it to @PNASNews — and yes, it can run a universal computer! 🎱💻 Undecidability already lives in dimension two. Today with @Isaacramr__ at PNAS. pnas.org/doi/10.1073/pnas.26…

This shall be an inflection point for us. Night helped me clarify my thoughts regarding the Navier-Stokes: 1. Martínez-Zoroa and Córdoba deserve the Fields in addition to other prizes. We should be honoring their work. 2. They Clay could (is it possible?): (i) be shared between M-Z and Córdoba (80%) + Buckmaster and Alpöge (20% -even when, personally, it feels bittersweet) -inclusive- or (ii) restated: no external-force. 3. Open AI shall face severe consequences if accusations are true. 4. We, the individuals of a small community -just us: math/math phys. students, professors, researchers-, independently from institutions, governments and companies, may hold closed-private but informal meetings to decide how we are willing to work from now on. I know some of us will choose to pursue a modest path: free from the publish-or-perish practice, AI proofs, stupid competition for recognition and money, etc. From that, we can build something real. 5. We, as a whole society, must be aware of the plausible future scenarios whether the statu quo remains unchanged: who has the majority of agency (power) regarding public affairs including knowledge, education, technology, violence control, justice management, etc.? Is it optimal or even safe? Meanwhile, let’s honor the work of those who deserve it: arxiv.org/pdf/2309.08495 arxiv.org/pdf/2308.12197 arxiv.org/pdf/2207.14385 arxiv.org/pdf/2410.22920

It's only real Navier-Stokes if it comes from the Navier-Stokes region of Courant. Otherwise it's just sparkling Euler equations.

I wrote about why the existence and smoothness of Navier-Stokes is still open, even though the Millennium problem was solved. I also explain how the proof worked (it's surprisingly simple) and what I think it means for the future of AI in science. nickmcgreivy.substack.com/p/…

It's been a while ! I've just publish a new post: 𝐆𝐚𝐮𝐬𝐬-𝐒𝐞𝐢𝐝𝐞𝐥 𝐢𝐬 𝐟𝐚𝐬𝐭𝐞𝐫 𝐭𝐡𝐚𝐧 𝐉𝐚𝐜𝐨𝐛𝐢. 𝐎𝐫 𝐢𝐬 𝐢𝐭? While keeping a high level p.o.v., I try to explain why Jacobi can be faster than Gauss-Seidel despite what the math says. tinyurl.com/yme7dahk

Here is my recent intro talk to masterclass on Koopman operator theory at the Isaac Newton Institute for Mathematical Sciences Cambridge, UK. piped.video/watch?v=mTSDXDlY… The talk was a part of the programme On Operator Theory Methods in Dynamical Systems newton.ac.uk/event/omd/ thanks to the Institute and the organizers!

Thrilled to share the story written by @MichiganAero on our recent Perspective on #ExplainableAI, #FoundationModels and #ScientificDiscovery! #Story: aero.engin.umich.edu/2026/08… @NatureComms: nature.com/articles/s41467-0… Great to work w/ @eigensteve @GMengaldo!!

Two weeks ago, Rikhav Shah and I posted a preprint on the growth factor in Gaussian elimination, and settled a very old problem. It turns out complete pivoting and rook pivoting have quasi-polynomial growth. I’ve spent a decade thinking about this problem. math.mit.edu/~urschel/prepri…

New #Video! We explain the method behind zero-shot DRL, where we train #DRL controllers in simple geometries (e.g. channel flow) and then deploy the same policies without further training directly on a wing. Without loss of performance!! piped.video/iA3oGUdq7aw?si=dLtc… #AI4Science

Check out this NeurIPS workshop on explainable AI for science!!

NEW ARTICLE: “HydroGym trains, assesses AI for actively controlling fluid dynamics.” With more than 60 environments, the simulated proving ground aims to speed the development of AI controllers that optimize drag, lift, noise and heat management. news.engin.umich.edu/2026/08…

Nice story by @UMengineering on our HydroGym paper, published in @Nature! Delighted to see the feedback from the community! Look at the zero shot results below! news.engin.umich.edu/2026/08… #Paper: nature.com/articles/s41586-0… @MichiganAero #AI4Science

Reinforcement learning can learn control strategies in a cheap simulation, and transfer them directly to a much harder physical system. Christian Lagemann and coauthors introduce HydroGym, a large standardized platform for applying reinforcement learning to fluid dynamics. The ML contribution is more important than simply adding another RL controller. HydroGym provides more than 60 validated environments spanning laminar and turbulent flows, two- and three-dimensional geometries, multiple Reynolds numbers and different solver backends. That makes it possible to ask a much harder question: can an RL policy learn transferable physical control principles rather than overfitting to one simulation? The authors train a multi-agent controller only on a computationally inexpensive turbulent channel-flow surrogate and then deploy it zero-shot to the boundary layer of a three-dimensional wing. No retraining on the wing is required. The transferred policy reduces local skin-friction drag by about 38% and total drag by 11%, outperforming conventional opposition control. Training in the surrogate also reduces the computational exploration cost by more than four orders of magnitude. Scientifically, the result suggests that the agent has captured something reusable about near-wall turbulence: control strategies learned in one geometry can survive a large change in geometry and Reynolds number when the underlying physics is shared. For scientific ML, this may be one of the most important roles of benchmark environments: not merely comparing algorithms, but discovering which learned policies encode transferable physics. Paper: Lagemann et al., Nature (2026), CC BY-NC-ND 4.0 | doi.org/10.1038/s41586-026-1…

The HydroGym computational environment teaches agents strategies for fluid-flow control that can be applied to scenarios they have not encountered before go.nature.com/4xR6NPZ

Nature research paper: The HydroGym reinforcement learning platform for fluid dynamics go.nature.com/4x3XiNb