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

arXiv: https://arxiv.org/abs/2505.16992 · HTML: https://mlsanity.com/paper/2505.16992/

## 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 (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Scientific multi-agent reinforcement learning for wall-models of turbulent flows](https://mlsanity.com/paper/2106.11144/) (2021)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)](https://mlsanity.com/paper/1911.09145/) (2019)
- [Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons](https://mlsanity.com/paper/2202.06988/) (2022)
- [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.05320/) (2023)
- [Differentiable hybrid neural modeling for fluid-structure interaction](https://mlsanity.com/paper/2303.12971/) (2023)
- [Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations](https://mlsanity.com/paper/2409.00230/) (2024)
- [PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence](https://mlsanity.com/paper/2105.08633/) (2021)
- [Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics](https://mlsanity.com/paper/2307.13533/) (2023)
- [Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning](https://mlsanity.com/paper/2309.06260/) (2023)
- [Physics-Guided Actor-Critic Reinforcement Learning for Swimming in Turbulence](https://mlsanity.com/paper/2406.10242/) (2024)

## Built on by (most cited first, 6 of 6)

- [Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control](https://mlsanity.com/paper/2601.15015/) (2026)
- [Case study of a differentiable heterogeneous multiphysics solver for a nuclear fusion application](https://mlsanity.com/paper/2511.13262/) (2025)
- [Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems](https://mlsanity.com/paper/2605.04708/) (2026)
- [PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectives](https://mlsanity.com/paper/2605.11266/) (2026)
- [Mosaic: A Benchmark Suite for Differentiable Physics Solvers](https://mlsanity.com/paper/2606.27895/) (2026)
- [CraftSPH: A high-accuracy and composable differentiable SPH solver implemented in PyTorch](https://mlsanity.com/paper/2609.38208/) (2026)

## 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.