Excited to see @Reuters cover the launch of our startup Accelerated Understanding.
We are training large scale AI models that can simulate and understand physics to invent and discover. Our models understand the world directly in 4D (3D + time) and across physical phenomena. Going full 4D requires massive context length, we have pushed it to a Trillion in training and exceeding 5 Trillion at inference.
AI giving you a bigger haystack of ideas doesn’t help. The bottleneck for new inventions and discoveries is shifting from ideas to the ability to test them. With AI that can simulate and understand physics we are directly attacking this bottleneck.
People have been trying to do this for a while now, but usually by taking shortcuts. Narrow surrogates are great if you happen to have enough of precisely the right data and your design loop stays in distribution. Video models look fantastic but sweep physical accuracy under the rug, and some static world models cut out physics altogether. A lot of interesting physics isn’t visual.
What does not cutting corners look like? Space stays 3D and you also have time: so 4D in total. You also need multiple physical modalities in the same model, not just things you can see. That’s what we’ve built.
Scaling is the primary ingredient to make this work. To represent the world you need sufficient context, which in our case grows in 4 dimensions. Individual samples get so big they don’t fit into single accelerators or even full nodes anymore.
We’ve developed architectural tricks to make it work. We’ve pushed our models to 1T parameters during large scale pre-training and are able to train at up to a Trillion context when needed and do inference exceeding 5 Trillion context without any sub-sampling or patching.
Building on prior successes of AI weather forecasting, fusion simulation, design of medical devices, drugs and chips, we wanted to see if scale and universality can benefit AI for physical understanding. With our teams’ experience in large-scale infrastructure and model training we’ve been able to pull it off.
https://t.co/w12yG9fCps
https://t.co/vWnPiTbLEy
@accelerated_u@bjenik
HydroGym: A Reinforcement Learning Platform for Fluid Dynamics
Now published in Nature!! https://t.co/o1zTn2DIHg
GitHub: https://t.co/9MLBzJAMiJ
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
Our new work on “Physics of Agents” https://t.co/qKo3O77kZ9 lead by Batu El and Jinhee Paeng in collab w/ @james_y_zou
The outcome of many interacting agents seems hard to reason about. Yet we were able to study the opinion dynamics of 10,000 different LLM agent communities as they communicated with each other to solve both objective and subjective questions.
Remarkably, we could account for their opinion dynamics through a simple Ising model that involved minimizing an energy function corresponding to social pressure to conform. Our dynamics could explain the build up of consensus, polarization, and societal correction of initially incorrect majorities.
Lots more to do on statistical mechanics of interacting agent dynamics!
I started in physics with numerical simulations, then accidentally found my way into ML.
This Caltech SURF project let me bring those ideas back to physics beyond textbooks. The journey was nonlinear, full of surprising empirical and theoretical discoveries.
Grateful for the guidance and opportunity.
A formative experience at the frontier of computational physics × generative models.
Solving Inverse PDEs with 1% Paired Data: Introducing Decoupled Diffusion Inverse Solver
We propose a data-efficient and physics-aware diffusion framework for solving inverse problems on function spaces.
In scientific machine learning, solving inverse problems requires costly and limited data acquisition from physical systems. Existing joint-embedding diffusion models require massive paired training data, as they represent the underlying physics implicitly through statistical correlations. In this work, we identify that under data scarcity, the observation-induced guidance signal vanishes during posterior sampling, making reconstruction impossible.
Our Solution: We propose a decoupled design against joint-embedding: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance. This enables (1) superior data efficiency (2) effective physics-informed learning and sampling.
Performance: Achieves state-of-the-art results on Navier-Stokes, Helmholtz, and Poisson benchmarks, improving spectral error by 54% on average.
Data Efficiency: DDIS maintains high accuracy even when limited to just 1% of paired training data, outperforming joint models by 40% in L2 error.
Robustness: Theoretical guarantees that avoid the guidance attenuation identified in joint-embedding methods.
Check out the paper for the full theoretical analysis and experiments!
https://t.co/B4MMhUlcjh
Thomas Lin , @jiacheny7, Alex Chiang, Julius Berner,
#MachineLearning #DiffusionModels #InverseProblems #PDE #NeuralOperators @Caltech #AI4Science
Tired to go back to the original papers again and again? Our monograph: a systematic and fundamental recipe you can rely on!
📘 We’re excited to release 《The Principles of Diffusion Models》— with @DrYangSong, @gimdong58085414, @mittu1204, and @StefanoErmon.
It traces the core ideas that shaped diffusion modeling and explains how today’s models work, why they work, and where they’re heading.
🧵You’ll find the link and a few highlights in the thread.
We’d love to hear your thoughts and join some discussions!
⚡ Stay tuned for our markdown version, where you can drop your comments!
The hot topic at #ICCV2025 was World Models.
They come in different flavors — (interactive) video models, neural simulators, reconstruction models, etc. — but the overarching goal is clear: Generative AI that predict and simulate how the real world works.
Feel like my learning curve on some math topics is mostly driven by chance. It’s so easy to fall into a rabbit hole (like endless Wikipedia pages) at first glance, but after a few weeks I accidentally met the same topic again, it feels utterly easy and intuitive.