mlsanityData to 14 Oct 2026

PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamics

arXiv 2505.16992 ↗First posted 22 May 2025cs.LG physics.comp-phcited by 6

Not on the map. Why?

Abstract (arXiv)

Despite decades of advancements, the simulation of fluids remains one of the most challenging areas of in scientific computing. Supported by the necessity of gradient information in deep learning, differentiable simulators have emerged as an effective tool for optimization and learning in physics simulations. In this work, we present our fluid simulator PICT, a differentiable pressure-implicit solver coded in PyTorch with Graphics-processing-unit (GPU) support. We first verify the accuracy of both the forward simulation and our derived gradients in various established benchmarks like lid-driven cavities and turbulent channel flows before we show that the gradients provided by our solver can be used to learn complicated turbulence models in 2D and 3D. We apply both supervised and unsupervised training regimes using physical priors to match flow statistics. In particular, we learn a stable sub-grid scale (SGS) model for a 3D turbulent channel flow purely based on reference statistics. The low-resolution corrector trained with our solver runs substantially faster than the highly resolved references, while keeping or even surpassing their accuracy. Finally, we give additional insights into the physical interpretation of different solver gradients, and motivate a physically informed regularization technique. To ensure that the full potential of PICT can be leveraged, it is published as open source: https://github.com/tum-pbs/PICT.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 24 of its 89 references that are in the map. First posted on arXiv 22 May 2025.

Builds on

24 of 89 references.

References · 24

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  3. 2021Machine learning accelerated computational fluid dynamicscited by 471
  4. 2021Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulationcited by 407
  5. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 267
  6. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 258
  7. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 205
  8. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 150
  9. 2020Learning to Control PDEs with Differentiable Physicscited by 132
  10. 2016Accelerating Eulerian Fluid Simulation With Convolutional Networkscited by 130
  11. 2021Scientific multi-agent reinforcement learning for wall-models of turbulent flowscited by 52
  12. 2020Convolutional-network models to predict wall-bounded turbulence from wall quantitiescited by 47
12 more
  1. 2019DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)cited by 41
  2. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  3. 2022JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flowscited by 36
  4. 2018Deep Neural Networks for Data-Driven Turbulence Modelscited by 35
  5. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  6. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 23
  7. 2023Differentiable hybrid neural modeling for fluid-structure interactioncited by 18
  8. 2024Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observationscited by 13
  9. 2021PDE-constrained Models with Neural Network Terms: Optimization and Global Convergencecited by 12
  10. 2023Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physicscited by 9
  11. 2023Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learningcited by 5
  12. 2024Physics-Guided Actor-Critic Reinforcement Learning for Swimming in Turbulencecited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 5.

6 papers.

  1. 2026Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Controlcited by 2
  2. 2025Case study of a differentiable heterogeneous multiphysics solver for a nuclear fusion applicationcited by 0
  3. 2026Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systemscited by 0
  4. 2026PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectivescited by 0
  5. 2026Mosaic: A Benchmark Suite for Differentiable Physics Solverscited by 0
  6. 2026CraftSPH: A high-accuracy and composable differentiable SPH solver implemented in PyTorchcited by 0