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e demonstrates strong fine tuning performance across various downstream tasks highlighting its versatility and effectiveness as a foundation model for 3d pde learning 2026 04 28 ge_at_tum stability and resolvent analysis of non linear systems via nns we d like to highlight our recent work on how useful nns are for stability and resolvent analysis of non linear systems https arxiv org abs 2604 19465 this is a very fundamental and classic topic and chengyun established a firm connection between the theoretical basis and modern ai methods importantly it shows how the differentiability of nns enables explainability and analysis of complex dynamical systems investigating how complex systems respond to perturbations remains a central challenge in both science and engineering traditional analysis methods are limited to simple linearized systems or require explicit governing equations we introduce a general data driven framework that uses neural networks to automatically discover the stability and receptivity properties of any system our approach identifies which perturbations will grow unstably near an equilibrium state and crucially pinpoints the optimal way to force the system to elicit the most amplified responses resolvent analysis even for strongly nonlinear systems this framework is potentially relevant to applications in fields ranging from climate science and neuroscience to fluid engineering particularly where first principles models are often intractable but sufficiently rich trajectory data is available source code examples are available https github com tum pbs nonlinearra 2026 04 22 2026 04 22 ge_at_tum foundation model paradigms for aerodynamic prediction we would like to share our latest work aerotransformer a step toward bringing the foundation model paradigm to real world aerodynamic design code models https github com tum pbs aerotransformer paper https arxiv org abs 2604 18062 modern engineering workflows still rely on expensive cfd simulations especially in 3d where generating training data is a major bottleneck aerotransformer tackles this by combining large scale pretraining efficient fine tuning enabling accurate predictions with drastically reduced data requirements key contributions a transformer based architecture tailored for large scale aerodynamic learning pretraining on diverse geometries 30k samples to capture global flow priors task specific fine tuning with only a few hundred samples establishing a pathway toward foundation models for engineering cfd the proposed approach achieves 1 2 relative error for new geometries drag coefficient reduces error by 84 vs training from scratch demonstrates strong generalization to new wing configurations this work reinforces a central shift instead of training task specific models from scratch each time we can pretrain once and then adapt the model with a small dataset 2026 04 20 ge_at_tum one scale at a time scale autoregressive modeling for fluid flow distributions sar ever wondered if a transformer model could successively refine a pde solution mario s latest work as a post doc at tum shows a way forward a single model auto regressively infers and refines flow solutions over finer and finer sets of sample points preprint of this sar approach and code are already online https arxiv org pdf 2604 11403 and https github com tum pbs sar in more detail understanding time dependent fluid flows often requires knowing not just a single solution but the full range of possible states over time however traditional pde solvers are very expensive to run and learned surrogate models that predict the next time step tend to accumulate errors when applied repeatedly over long time horizons generative models offer an alternative by directly sampling flow states without relying on sequential time stepping thereby avoiding error accumulation however existing approaches such as diffusion or flow matching models remain computationally costly as they require many evaluations across the entire spatial domain scale autoregressive modeling sar addresses this limitation by generating flow fields in a hierarchical coarse to fine manner it first predicts a low resolution version of the flow and then progressively refines it to higher resolutions conditioning each step on the previous coarser prediction this strategy improves efficiency by focusing most of the computational effort on coarse scales where uncertainty is highest importantly it requires fewer denoising steps at finer scales across unsteady flow benchmarks of varying complexity sar attains substantially lower distributional error and higher per sample accuracy than state of the art diffusion models based on multi scale gnns while matching or surpassing a flow matching transformer yet running 2 7x faster than it depending on the task overall sar provides a practical tool for fast and accurate estimation of statistical flow quantities e g turbulent kinetic energy and two point correlations in real world settings 2026 04 13 ge_at_tum p3d pde transformer in 3d code weights release we d like to highlight the code release of our scalable efficient pde transformer p3d at https akanota github io p3d great work benjamin with support from florian georg please try out the pretrained models and let us know how it works highlights are e g stable inference of 1024 3 rollouts on a single gpu with 90gb key contributions hybrid cnn transformer p3d combines convolutions for fast local features with windowed self attention for deep representation learning in a hierarchical u shape structure scalable pretraining pretrain on small 128³ crops then scale to the full 1024³ domain reducing memory and compute while maintaining accuracy global context network a sequence to sequence model links bottleneck layers for efficient global information processing with region tokens for direct decoder feedback probabilistic generation train p3d as a diffusion model to produce probabilistic samples of turbulent channel flows accurately capturing flow statistics across reynolds numbers links main page https akanota github io p3d paper https openreview net forum id 8udce5nhfl code https github com tum pbs p3d weights data https huggingface co thuerey group p3d 2026 02 09 ge_at_tum iclr 2026 physics based flow matching accepted we re happy to report that our physics based flow matching framework got an accept for iclr 26 we target the fundamental trade off between physical consistency and distributional fidelity in generative modeling by proposing physics based flow matching pbfm a principled framework that explicitly targets pareto optimal solutions between physics constraints and data driven objectives pbfm builds on flow matching and enforces pde and algebraic constraints during training using conflict free gradient updates via the config optimizer we address the long standing jensen s gap by unrolling the learned dynamics during training ensuring that physical residuals are evaluated on accurate final samples without slowing down inference across three challenging benchmarks darcy kolmogorov flows and highly nonlinear dynamic stall pbfm consistently advances the pareto front achieving lower physical residuals and better distributional accuracy than prior physics informed diffusion and flow based methods at the same time it preserves the key advantage of flow matching fast scalable inference with performance comparable to unconstrained generators we frame physics constrained generative modeling as a multi objective optimization problem to deliver a practical solution pbfm demonstrates that high fidelity uncertainty aware generative models can be both physically meaningful and statistically correct this makes them a powerful tool for real world applications in science and engineering code and paper can be found here https github com tum pbs pbfm https arxiv org abs 2506 08604 2026 02 07 ge_at_tum source code for fast rotational equivariance for physics gnns sb gnns fast rotational equivariance for physics gnns the source code for our paper on rotational equivariant graphnets via local eigenbases is now available https github com tum pbs strain base gnn we introduce a basis transformation approach sb gnns that preserves full geometric and physical information while avoiding the heavy computational cost of conventional equivariant layers across three challenging pde benchmarks our method matches sota accuracy consistently outperforms data augmentation and delivers order of magnitude efficiency gains in practice if you re interested in ml for pdes cfd or equivariant learning the code and test cases are ready to use and build upon let us know how it works for you please check out the full physics of fluids paper here https pubs aip org aip pof article 37 8 087178 3359552 rotational equivariant graph neural networks via 2026 02 03 2026 03 18 ge_at_tum iclr 2026 p3d transformer accepted we re very excited to report that our p3d transformer was accepted at iclr https openreview net forum id 8udce5nhfl in the paper we introduce a scalable hybrid cnn transformer architecture that pushes neural surrogate modeling into the regime of truly high resolution 3d simulations by combining fast local convolutions with carefully designed attention and an optional global context model the p3d architecture overcomes previous memory and compute barriers that have limited transformers for pde problems p3d is trained on small 3d crops but seamlessly assembles them into coherent large scale solutions we show that p3d can learn multiple different types of pde dynamics in 3d simultaneously and that it outperforms state of the art neural operators and transformers in both accuracy and efficiency beyond deterministic prediction p3d also works as a probabilistic generative model trained via flow matching diffusion it produces high fidelity samples of turbulent channel flows across varying reynolds numbers capturing correct velocity profiles and higher order statistics while being orders of magnitude faster than dns code and pre trained models will be up soon thanks again to the nhr fau hpc center and its team for the support it was great that we received compute time on helma for this project impressive performance 2026 01 30 2026 01 30 ge_at_tum acdm autoregressive diffusion models accepted in neural networks journal 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 three years later and after several other stages finally got into neural networks https www sciencedirect com science article pii s0893608026001036 despite the long wait i think the main conclusions of our paper are still valid even vanilla diffusion flow matching models without special modifications perform great for time predictions deterministic models with proper unrolling can match them importantly both can lead to unconditionally stable surrogates ie nn operators that don t blow up code benchmark can be found here https github com tum pbs autoreg pde diffusion 2026 01 24 2026 01 24 ge_at_tum fluidgym reinforcement learning control of 3d fluid flows with pict there is enormous potential for reinforcement learning and other data driven control paradigms for controlling large scale fluid flows but rl research on such systems is often hindered by a complex and brittle software pipeline consisting of external solvers and multiple code bases making this exciting field inaccessible for many rl researchers to tackle this challenge we primarily jannis from tu dortmund have developed a standalone fully differentiable plug and play benchmark for rl in active flow control implemented in a single pytorch codebase via pict without external solver dependencies our fluidgym comes with a collection of standardized environment configurations spanning diverse 3d and multi agent control tasks we perform an extensive experimental study with multiple seeds randomized initial conditions and separate train validate test sets we compare the default implementations of the two most popular algorithms ppo and sac in the single and multi agent settings and also investigate the potential for transfer learning we hope that this may be of interest to a large number of reinforcement learning researchers who are keen on assessing the most recent trends in basic rl research on a new set of challenging tasks but otherwise find it difficult to enter the field of fluid mechanics repository https github com safe autonomous systems fluidgym paper https arxiv org abs 2601 15015 2026 01 09 ge_at_tum physics constrained reconstruction super resolution with generative models our paper on physics constrained reconstruction super resolution with generative models was posted online now at https doi org 10 1063 5 0304492 this paper started out as a master thesis by marc trepat was continued with luis thesis and turned out to work exceptionally well pde transformer as an accurate efficient backbone architecture https tum pbs github io pde transformer landing html differentiable physics constraints to guide the generative model https ge in tum de publications 2020 um solver in the loop and config as optimizer to resolve conflicts in the gradients https tum pbs github io config source code is available at https github com tum pbs sparse reconstruction let us know how it works for you 2025 12 17 ge_at_tum superwing dataset large scale realistic aerodynamics for ai machine learning 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 https arxiv org abs 2512 14397 it offers more complex geometry kinked wings and larger parametric variety than all existing 3d airfoil datasets created primarily by yunjia and collaborators from tsinghua university the huggingface dataset https huggingface co datasets yunplus superwing captures strong and challenging variations in spanwise shape twist and dihedral angles offering unprecedented geometric diversity transformer models trained on superwing achieve low drag prediction errors and show strong zero shot generalization to canonical aircraft configurations positioning superwing as a key resource for data driven aerodynamic modeling full abstract machine learning surrogate models have shown promise in accelerating aerodynamic design yet progress toward generalizable predictors for three dimensional wings has been limited by the scarcity and restricted diversity of existing datasets here we present superwing a comprehensive open dataset of transonic swept wing aerodynamics comprising 4 239 parameterized wing geometries and 28 856 reynolds averaged navier stokes flow field solutions the wing shapes in the dataset are generated using a simplified yet expressive geometry parameterization that incor...
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