We're happy to report that our Physics-based Flow Matching framework got an accept for ICLR'26! Physics-Based Flow Matching (PBFM) is a principled framework that explicitly targets Pareto-optimal solutions between physics-constraints and data-driven objectives.

Fast rotational equivariance for physics GNNs — the source code is now available: github.com/tum-pbs/stra... Please also check out the full Physics-of-Fluids paper here: pubs.aip.org/aip/pof/arti...

We're very excited to report that our P3D Transformer was accepted at ICLR openreview.net/forum?id=8Ud... We introduce a scalable hybrid CNN–Transformer architecture that pushes neural surrogate modeling into the regime of truly high-resolution 3D simulations.

I'm very happy to report that our autoregressive predictions with generative diffusion models is _finally_ accepted 😁 Congratulations Georg! It's been a long journey, this paper was first submitted to NeurIPS'23, and now, almost 3y later, finally got accepted www.sciencedirect.com/science/arti...

Great to see our paper on physics-constrained reconstruction / super-res with generative models posted online now at doi.org/10.1063/5.03... 😁 - PDE Transformer as backbone architecture - differentiable physics constraints to guide - and ConFIG as optimizer to resolve conflicts in the gradients

The SuperWing dataset is a large-scale, open dataset of transonic swept-wing aerodynamics, combining thousands of richly parameterized 3D wing geometries with high-fidelity RANS simulations across the operational flight envelope: arxiv.org/abs/2512.14397

Please join our mini symposium on "AI for Computational Fluid Dynamics - Opportunities and Challenges" MS279 , wccm-eccomas2026.org/event/area/8... at WCCM ECCOMAS in Munich next year in July (July 2026, wccm-eccomas2026.org). Inspiring discussions, and a proper "Mass" at the beergarden 🍻😁

Our full course "advanced deep learning for physics" (ADL4P) is online now at tum-pbs.github.io/ADL4P/ 😁 The course covers AI and neural network techniques for physics simulations & combinations with numerical methods. All recordings, slides and exercises are freely available!

Can AI surrogates outperform their training data? Turns out the answer is yes - with a few caveats 😉 tum-pbs.github.io/emulator-sup... #neurips This surprising behavior leads to interesting and fundamental questions about the role of training data, and about how NN surrogates should be evaluated.

Can your AI surpass the simulator that taught it? What if the key to more accurate PDE modeling lies in questioning your training data's origins? 🤔 Excited to share my #NeurIPS 2025 paper with @thuereygroup.bsky.social: "Neural Emulator Superiority"!

Congratulations to Hao, Aleksandra and Bjoern for their NeurIPS paper tum-pbs.github.io/inc-paper/ 👍 It analyzes how hybrid PDE solvers fundamentally and provably benefit from "indirect" (force-based) corrections rather than direct ones. Baking the corrections via INC reduces error growth!

I wanted to highlight that source code and data for our physics-based flow matching (PBFM) algorithm are online now at: github.com/tum-pbs/PBFM/ feel free to give it a try, and we'd be curious to hear how it works for you!

I'm happy to report that our collaborative project on 3D sparse-reconstruction and super-resolution with diffusion models, physics constraints and PDE Transformers is online now as preprint arxiv.org/abs/2510.19971 and source code github.com/tum-pbs/spar.... Great work Marc, Luis, Qiang and Luca 👍

I'm very excited to introduce P3D: our PDE-Transformer architecture in 3 dimensions by . Demonstrated for unprecedented 512^3 resolutions! That means the Transformer produces over 400 million degrees of freedom in one go 😀 a regime that was previously out of reach: arxiv.org/abs/2509.10186

Congratulations to Bjoern for his accepted PoF paper on equivariant GraphNets 👍 doi.org/10.1063/5.02... the core idea is a very generic and powerful one: we compute a local Eigenbasis from flow features for equivariance. Mathematically it's identical to previous approaches, but faster and simpler 😅

I also wanted to mention that our paper detailing the differentiable SPH solver by Rene is online now on arxiv: arxiv.org/abs/2507.21684 If you're interested in fast and efficient neighborhoods, differentiable SPH operators and neat first optimization and learning tasks, please take a look!

Get ready for the PDE-Transformer: our new NN architecture tailored to scientific tasks 😁 It combines hierarchical processing (UDiT), scalability (SWin) and flexible conditioning mechanisms. Code and paper available at tum-pbs.github.io/pde-transfor...

I'm really excited to share our latest work combining physics priors with probabilistic models: Flow Matching Meets PDEs - A Unified Framework for Physics-Constrained Generation , arxiv.org/abs/2506.08604 , great work by Giacomo and Qiang!

Have you faced challenges like SPH-based inverse problems, or learning Lagrangian closure models? For these we’re excited to announce the first public release of DiffSPH , our differentiable Smoothed Particle Hydrodynamics solver. Code: diffsph.fluids.dev Short demo: lnkd.in/dYABSeKG

Congratulations to Bernhard for his first #SIGGRAPH paper! Great work 👍 His two-phase Navier-Stokes solver is even more impressive given the fact that it's all done on a regular workstation, and without a GPU. Enjoy the sims in full screen & hi-quality here: youtu.be/nt9BohngvoE

I also just recorded a quick overview video for our new PICT solver: youtu.be/GGLidL0oT3s , enjoy! In case you missed it: PICT provides a new fully-differentiable multi-block Navier-Stokes solver for AI and learning tasks in PyTorch, e.g. learning turbulence closure in 3D

I'd like to highlight PICT, our new differentiable Fluid Solver built for AI & learning: github.com/tum-pbs/PICT Simulating fluids is hard, and learning 3D closure models even harder: This is where PICT comes in — a GPU-accelerated, fully differentiable fluid solver for PyTorch 🥳

I can highly recommend checking out Mario's talk about our Diffusion Graph Net paper from ICLR'25: www.youtube.com/watch?v=4Vx_... , enjoy!

I wanted to highlight PBDL's brand-new sections on diffusion models with code and derivations! Great work by Benjamin Holzschuh, with neat Jupyter notebooks 👍 All the way from normalizing flow basics over score matching to denoising & flow matching. E.g., colab.research.google.com/github/tum-p...

If you're at #ICLR 2025 in Singapore, please check out our posters 🤗 I'm sure it's going to be a great conference! Have fun everyone...

I wanted to highlight that our project website (with code!) for our progressively-refined training with physics simulations is up now at: kanishkbh.github.io/prdp-paper/ #ICLR25 , the main ideas are: match network approximation and physics accuracy, refine the physics over the course of training.

The full PBDL book is available in a single PDF now arxiv.org/pdf/2109.05237, and has grown to 451 pages 😳 Enjoy all the new highlights on generative models, simulation-based constraints and long term stability with diffusion models 😁

I'm very excited to highlight PBDL v0.3 www.physicsbaseddeeplearning.org, the latest version of our physics-based deep learning "book" 🥳 This version features a huge new chapter on generative AI, covering topics ranging from the derivation, over graph-based inference to physics-based constraints!

Congratulations to Kanishk and Felix 👍 for their #ICLR'25 paper "Progressively Refined Differentiable Physics" kanishkbh.github.io/prdp-paper/ , the key insight is that training can be accelerated substantially by using fast approximates of the gradient (especially in early phases of training)

Congratulations to Youssef and Benjamin 👍 for their #ICLR'25 paper on Truncated Diffusion Sampling openreview.net/forum?id=0Fb... It investigates several key questions of generative AI and diffusion for physics simulations to improve accuracy via Tweedie's formula

Can AI Help Solve Complex Physics Equations? Meet APEBench, an innovative benchmark suite introduced by our Junior Member Felix Köhler, together with our PIs Rüdiger Westermann and Nils Thuerey as well as co-author Simon Niedermayr. Read more: mcml.ai/news/2025-02...

Congratulations also to Patrick 👍 for his ICLR paper on Temporal Difference (TD) learning openreview.net/forum?id=j3b... , in it We solve the decades-old puzzle of why TD can solve complex RL tasks that Gradient Descent cannot. Our novel theory shows for 2D how TD can counter ill-conditioning 🤗

Congrats to Qiang 👏 for the accept of his #ICLR paper on the "ConFIG" optimizer openreview.net/forum?id=APo... Conflict free learning for PINNs, multi task objectives and more! Outperforms all existing optimizers 😁 source code and examples are online at tum-pbs.github.io/ConFIG/

Regarding our 'Diffusion Graph Net' paper at #ICLR'25 openreview.net/forum?id=uKZ..., it's also worth mentioning that the full source code is already online github.com/tum-pbs/dgn4... , complete with notebooks, flow matching, and the full hierarchical diffusion graph net architecture 😁

Congrats to Mario 👏 for the accept of his ICLR paper on "Diffusion Graph Nets", it targets predicting complex distributions of flow states on unstructured meshes openreview.net/forum?id=uKZ... It works even if the training data contains only a fraction of the flow statistics per case.

I’d like to thank everyone contributing to our five accepted ICLR papers for the hard work! Great job everyone 👍 Here’s a quick list, stay tuned for details & code in the upcoming weeks…

Out of curiosity, I recently re-ran the KS equation tests in our "unrolling" paper (github.com/tum-pbs/unro...), and interestingly the effects are even stronger with long training. Up to 10x now for relative errors:

Liwei's paper on deep learning-based predictive modeling of airfoil flows is online at PoF now doi.org/10.1063/5.02... 👍 Long-term stability 🐎 and correct transition from mean flow. Linear stability analysis 📉 of the NN Jacobians around the mean confirms the accuracy of the trained operator ⭐️

I will be presenting my poster on APEBench on Thursday from 11:00 to 14:00 PST at West Ballroom A-D #5407. This was done as part of my PhD with @thuereygroup.bsky.social in collaboration with my talented co-author, Simon Niedermayr, who is supervised by Rüdiger Westermann.

If you're training models with more than one loss term, I can again strongly recommend our ConFIG optimizer: tum-pbs.github.io/ConFIG/ , simply swap out Adam&Co. for ConFIG, and you can potentially see substantial reductions in your training loss 😁 We'd also be curious to hear how it works for you

Our APEBench tum-pbs.github.io/apebench-pap... actually comes with an integrated GPU-based volume renderer "VAPE" (keksboter.github.io/vape4d/), that works in your browser (and in Jupyter). If you're patient, try it here (this link downloads 100MB): vape.niedermayr.dev?file=https:/...

I also wanted to highlight our new PBDL dataset project github.com/tum-pbs/pbdl.... It provides convenient access to our training cases, e.g. our "classic" airfoil learning example is very concise now: colab.research.google.com/github/tum-p... More datasets to follow soon 😀

I'm excited to share our APEBench paper arxiv.org/abs/2411.00180 and code github.com/tum-pbs/apeb..., to be presented at #NeurIPS. Congratulations Felix and Simon 😀 👍 At its core, APEBench features a lightning-fast ⚡️ fully differentiable spectral solver with a huge range of different PDEs.

Ever wondered how to turn your denoising diffusion code into flow matching? 🤔 Or what all the fuss regarding diffusion models was about in the first place? 🧐 Check out our new PBDL Jupyter notebook: colab.research.google.com/github/tum-p... 😎

I'm excited to share our paper "Flow Matching for Posterior Inference with Simulator Feedback" arxiv.org/abs/2410.22573 🤩 The key idea is to incorporate physics-constraints with guiding so that the posterior isn't becoming biased. Gives highly accurate solutions quickly, better than pure learning!

Yay, our paper on training recurrent Neural operators with a solver-in-the-loop was finally officially accepted at CMAME! Congratulations Bjoern 😀 👍 In parallel, we've been updating the paper arxiv.org/pdf/2402.12971 and the source code github.com/tum-pbs/unro... Feel free to give it a try!

We finally added a "proper" comparison for our airfoil diffusion models github.com/tum-pbs/Diff... , and still see almost 10x on the CPU, and another order of magnitude with the GPU.

"Fair" comparison between NNs and solvers can cause a lot of headache 🤯 I'd recommend to at least lower the fidelity of the solver. So _don't_ just compare with solver from the training data, the NN will have a higher error!

We have updated our diffusion-based airfoil project with flow matching arxiv.org/abs/2312.05320! It's clearly better: an improved distribution with fewer iterations. Try it for yourself in our new Jupyter notebook github.com/tum-pbs/Diff...

Our ConFIG method (tum-pbs.github.io/ConFIG/) is now on pip, you can install via "pip install conflictfree". And please try our examples such as the classic PINN Burgers case: colab.research.google.com/github/tum-p... With a small change you can directly decrease the loss by 16x 😀