Physics-Informed Neural Network Approaches for Sparse Data Flow Reconstruction of Unsteady Flow Around Complex Geometries

2025-08-02

AI Summary

This study addresses the challenge of reconstructing unsteady flow fields from sparse, measurement-driven data under computational resource constraints. We propose an enhanced physics-informed neural network (PINN) framework featuring dynamic loss weighting and progressive relaxation of physical constraints, significantly improving convergence and generalization in low-data-density regimes. By integrating standard PINN with a boundary-compatible BC-PINN architecture, the method ensures physical consistency of the reconstructed flow solutions without requiring extensive labeled training data. The approach is rigorously validated on two canonical complex-geometry problems: two-dimensional laminar flow around a circular cylinder and three-dimensional turbulent flow around an ultra-large container ship. Results demonstrate high-fidelity, robust time-resolved flow field reconstruction, thereby extending the engineering applicability of PINNs to high-dimensional, unsteady inverse fluid dynamics problems.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like computer vision and natural language processing, obtaining such datasets for engineering applications is prohibitively expensive. Physics-Informed Neural Networks (PINNs), a branch of Physics-Informed Machine Learning (PIML), tackle this challenge by embedding physical principles within neural network architectures. PINNs have been extensively explored for solving diverse forward and inverse problems in fluid mechanics. Nonetheless, there is limited research on employing PINNs for flow reconstruction from sparse data under constrained computational resources. Earlier studies were focused on forward problems with well-defined data. The present study attempts to develop models capable of reconstructing the flow field data from sparse datasets mirroring real-world scenarios. This study focuses on two cases: (a) two-dimensional (2D) unsteady laminar flow past a circular cylinder and (b) three-dimensional (3D) unsteady turbulent flow past an ultra-large container ship (ULCS). The first case compares the effectiveness of training methods like Standard PINN and Backward Compatible PINN (BC-PINN) and explores the performance enhancements through systematic relaxation of physics constraints and dynamic weighting of loss function components. The second case highlights the capability of PINN-based models to learn underlying physics from sparse data while accurately reconstructing the flow field for a highly turbulent flow.

Problem

• Reconstruct unsteady flow with sparse data using PINNs
• Compare training methods for 2D and 3D complex flows
• Enhance flow reconstruction accuracy under computational constraints

Innovation

• Physics-Informed Neural Networks for sparse data
• Dynamic weighting of loss function components
• Flow reconstruction from sparse turbulent data