# Geometry-aware PINNs for Turbulent Flow Prediction

arXiv: https://arxiv.org/abs/2412.01954 · HTML: https://mlsanity.com/paper/2412.01954/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 8 of 8)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Distributed physics informed neural network for data-efficient solution to partial differential equations](https://mlsanity.com/paper/1907.08967/) (2019)
- [Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks](https://mlsanity.com/paper/1705.09036/) (2017)
- [Frequency-compensated PINNs for Fluid-dynamic Design Problems](https://mlsanity.com/paper/2011.01456/) (2020)
- [RANS-PINN based Simulation Surrogates for Predicting Turbulent Flows](https://mlsanity.com/paper/2306.06034/) (2023)
- [Demystifying the Data Need of ML-surrogates for CFD Simulations](https://mlsanity.com/paper/2205.08355/) (2022)

## Abstract (arXiv)

Design exploration or optimization using computational fluid dynamics (CFD) is commonly used in the industry. Geometric variation is a key component of such design problems, especially in turbulent flow scenarios, which involves running costly simulations at every design iteration. While parametric RANS-PINN type approaches have been proven to make effective turbulent surrogates, as a means of predicting unknown Reynolds number flows for a given geometry at near real-time, geometry aware physics informed surrogates with the ability to predict varying geometries are a relatively less studied topic. A novel geometry aware parametric PINN surrogate model has been created, which can predict flow fields for NACA 4 digit airfoils in turbulent conditions, for unseen shapes as well as inlet flow conditions. A local+global approach for embedding has been proposed, where known global design parameters for an airfoil as well as local SDF values can be used as inputs to the model along with velocity inlet/Reynolds number (Re) to predict the flow fields. A RANS formulation of the Navier-Stokes equations with a 2-equation k-epsilon turbulence model has been used for the PDE losses, in addition to limited CFD data from 8 different NACA airfoils for training. The models have then been validated with unknown NACA airfoils at unseen Reynolds numbers.