# Deep Surrogate for Direct Time Fluid Dynamics

arXiv: https://arxiv.org/abs/2112.10296 · HTML: https://mlsanity.com/paper/2112.10296/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 16 Dec 2021.

## Builds on (most cited first, 18 of 18)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers](https://mlsanity.com/paper/2008.09768/) (2020)
- [Direct Prediction of Steady-State Flow Fields in Meshed Domain with Graph Networks](https://mlsanity.com/paper/2105.02575/) (2021)

## Built on by (most cited first, 5 of 5)

- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)
- [Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes](https://mlsanity.com/paper/2410.06406/) (2024)
- [Implicit Neural Representation For Accurate CFD Flow Field Prediction](https://mlsanity.com/paper/2408.06486/) (2024)
- [Scalar Field Prediction on Meshes Using Interpolated Multi-Resolution Convolutional Neural Networks](https://mlsanity.com/paper/2410.05522/) (2024)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)

## Abstract (arXiv)

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such simulations. The recent years have seen a surge of deep learning surrogate models substituting these solvers to alleviate the simulation process. Some approaches to build data-driven surrogates mimic the solver iterative process. They infer the next state of the fluid given its previous one. Others directly infer the state from time input. Approaches also differ in their management of the spatial information. Graph Neural Networks (GNN) can address the specificity of the irregular meshes commonly used in CFD simulations. In this article, we present our ongoing work to design a novel direct time GNN architecture for irregular meshes. It consists of a succession of graphs of increasing size connected by spline convolutions. We test our architecture on the Von K'arm'an's vortex street benchmark. It achieves small generalization errors while mitigating error accumulation along the trajectory.