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

arXiv: https://arxiv.org/abs/2503.15679 · HTML: https://mlsanity.com/paper/2503.15679/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Distributed physics informed neural network for data-efficient solution to partial differential equations](https://mlsanity.com/paper/1907.08967/) (2019)
- [Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foil](https://mlsanity.com/paper/2306.13395/) (2023)

## Built on by (most cited first, 2 of 2)

- [An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes](https://mlsanity.com/paper/2512.11860/) (2025)
- [Enhancing PINN Accuracy for the RLW Equation: Adaptive and Conservative Approaches](https://mlsanity.com/paper/2511.11638/) (2025)

## Abstract (arXiv)

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.