Sequential learning based PINNs to overcome temporal domain complexities in unsteady flow past flapping wings

2025-03-19

AI Summary

This work addresses the challenges of long-sequence velocity field reconstruction and pressure recovery for flapping-wing micro-air vehicles operating in unsteady flows with moving boundaries. Conventional physics-informed neural networks (PINNs) suffer from error accumulation and instability under temporal sparsity, long-time-domain integration, and broadband spectral response. To overcome these limitations, we propose a dual-sequence learning framework integrating temporal decomposition with transfer learning, coupled with immersed-boundary-aware PINNs and a prioritized spatiotemporal sampling strategy to enable piecewise training and suppress error propagation. The resulting segmented multi-subnetwork architecture reduces trainable parameters by over 30%, significantly enhancing long-duration simulation stability and aerodynamic force reconstruction accuracy while substantially lowering computational cost. Our method achieves high-fidelity pressure recovery and aerodynamic load reconstruction in unsteady flow modeling with moving boundaries.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

For a data-driven and physics combined modelling of unsteady flow systems with moving immersed boundaries, Sundar {it et al.} introduced an immersed boundary-aware (IBA) framework, combining Physics-Informed Neural Networks (PINNs) and the immersed boundary method (IBM). This approach was beneficial because it avoided case-specific transformations to a body-attached reference frame. Building on this, we now address the challenges of long time integration in velocity reconstruction and pressure recovery by extending this IBA framework with sequential learning strategies. Key difficulties for PINNs in long time integration include temporal sparsity, long temporal domains and rich spectral content. To tackle these, a moving boundary-enabled PINN is developed, proposing two sequential learning strategies: - a time marching with gradual increase in time domain size, however, this approach struggles with error accumulation over long time domains; and - a time decomposition which divides the temporal domain into smaller segments, combined with transfer learning it effectively reduces error propagation and computational complexity. The key findings for modelling of incompressible unsteady flows past a flapping airfoil include: - for quasi-periodic flows, the time decomposition approach with preferential spatio-temporal sampling improves accuracy and efficiency for pressure recovery and aerodynamic load reconstruction, and, - for long time domains, decomposing it into smaller temporal segments and employing multiple sub-networks, simplifies the problem ensuring stability and reduced network sizes. This study highlights the limitations of traditional PINNs for long time integration of flow-structure interaction problems and demonstrates the benefits of decomposition-based strategies for addressing error accumulation, computational cost, and complex dynamics.

Problem

• Addresses long time integration challenges in unsteady flow systems.
• Overcomes error accumulation in velocity and pressure reconstruction.
• Improves accuracy and efficiency in modeling flapping wing dynamics.

Innovation

• Sequential learning enhances PINNs for long time integration.
• Time decomposition reduces error propagation and computational complexity.
• Transfer learning improves accuracy in quasi-periodic flow modeling.