Simulating Three-dimensional Turbulence with Physics-informed Neural Networks

TL;DR

This paper demonstrates that physics-informed neural networks can effectively simulate complex three-dimensional turbulent flows directly from physical equations, offering a mesh-free alternative to traditional computational methods.

Contribution

The authors introduce novel algorithmic strategies enabling PINNs to accurately model fully turbulent flows in 2D and 3D without data or grids, advancing turbulence simulation techniques.

Findings

PINNs accurately reproduce turbulence statistics

The approach handles chaotic fluid dynamics effectively

Validated on challenging turbulence problems

Abstract

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically different approach that trains neural networks directly from physical equations rather than data, offering the potential for continuous, mesh-free solutions. Here we show that appropriately designed PINNs can successfully simulate fully turbulent flows in both two and three dimensions, directly learning solutions to the fundamental fluid equations without traditional computational grids or training data. Our approach combines several algorithmic innovations including adaptive network architectures, causal training, and advanced optimization methods to overcome the inherent challenges of learning chaotic dynamics. Through rigorous validation on challenging turbulence problems, we demonstrate that PINNs accurately reproduce key flow statistics including energy spectra, kinetic energy, enstrophy, and Reynolds stresses. Our results demonstrate that neural equation solvers can handle complex chaotic systems, opening new possibilities for continuous turbulence modeling that transcends traditional computational limitations.