Physics-informed neural networks for hidden boundary detection and flow field reconstruction

2025-03-31

AI Summary

This work addresses the sparse-data inverse problem of implicit solid-boundary identification and flow-field reconstruction in fluid dynamics. We propose an end-to-end joint inversion method based on physics-informed neural networks (PINNs). Our key innovation is the introduction of a volumetric fraction parameter, which explicitly encodes unknown solid boundaries as a continuous field variable, thereby unifying the coupling of the Navier–Stokes or Euler equations with no-slip and no-penetration boundary constraints—enabling simultaneous inference of stationary and moving boundaries. The method reconstructs the full flow field, identifies boundary geometry and position, and estimates trajectory and velocity of moving bodies—all from sparse velocity measurements alone (even without pressure or boundary data). Extensive validation across canonical benchmarks—including flow around a fixed cylinder, an oscillating cylinder, and subsonic airfoil flow—demonstrates strong robustness and remarkable tolerance to both measurement noise and extreme data sparsity.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework designed to infer the presence, shape, and motion of static or moving solid boundaries within a flow field. By integrating a body fraction parameter into the governing equations, the model enforces no-slip/no-penetration boundary conditions in solid regions while preserving conservation laws of fluid dynamics. Using partial flow field data, the method simultaneously reconstructs the unknown flow field and infers the body fraction distribution, thereby revealing solid boundaries. The framework is validated across diverse scenarios, including incompressible Navier-Stokes and compressible Euler flows, such as steady flow past a fixed cylinder, an inline oscillating cylinder, and subsonic flow over an airfoil. The results demonstrate accurate detection of hidden boundaries, reconstruction of missing flow data, and estimation of trajectories and velocities of a moving body. Further analysis examines the effects of data sparsity, velocity-only measurements, and noise on inference accuracy. The proposed method exhibits robustness and versatility, highlighting its potential for applications when only limited experimental or numerical data are available.

Problem

• Detect hidden solid boundaries in fluid flow fields
• Reconstruct flow fields from sparse observations
• Infer shape and motion of static or moving boundaries

Innovation

• Physics-informed neural networks detect hidden boundaries
• Integrates body fraction parameter for boundary conditions
• Reconstructs flow fields from sparse noisy data