Simulating Three-dimensional Turbulence with Physics-informed Neural Networks

2025-07-11

AI Summary

High-resolution 3D turbulent flow simulation is hindered by the prohibitive computational cost and grid dependency of conventional numerical methods. This work proposes a mesh-free solver framework based on physics-informed neural networks (PINNs), directly enforcing the Navier–Stokes equations without requiring training data or spatial discretization. The method innovatively integrates an adaptive network architecture, a causally structured temporal loss function, and gradient-based optimization strategies—enabling, for the first time, stable and high-fidelity PINN-based simulation of fully developed two- and three-dimensional turbulence across all scales. Validated on canonical turbulent flow benchmarks, the approach accurately reproduces key statistical quantities—including energy spectra, kinetic energy decay, vorticity structures, and Reynolds stresses—demonstrating its capability to model strongly nonlinear, chaotic systems. This advances a new paradigm for overcoming fundamental bottlenecks in classical computational fluid dynamics.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Neural Architectures and Foundation Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Simulating 3D turbulence with neural networks
• Overcoming high computational costs in fluid dynamics
• Learning chaotic dynamics without traditional grids

Innovation

• Physics-informed neural networks for turbulence simulation
• Mesh-free solutions from fundamental fluid equations
• Adaptive architectures and causal training methods