# Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foil

arXiv: https://arxiv.org/abs/2306.13395 · HTML: https://mlsanity.com/paper/2306.13395/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 73 references that are in the map.
- First posted on arXiv 23 Jun 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [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)
- [DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2112.14038/) (2021)
- [Failure-informed adaptive sampling for PINNs](https://mlsanity.com/paper/2210.00279/) (2022)
- [A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions](https://mlsanity.com/paper/2302.14227/) (2023)
- [SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functions](https://mlsanity.com/paper/1912.12355/) (2019)
- [Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data](https://mlsanity.com/paper/1808.04327/) (2018)
- [Deep learning of free boundary and Stefan problems](https://mlsanity.com/paper/2006.05311/) (2020)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)
- [RANG: A Residual-based Adaptive Node Generation Method for Physics-Informed Neural Networks](https://mlsanity.com/paper/2205.01051/) (2022)
- [Loss Landscape Engineering via Data Regulation on PINNs](https://mlsanity.com/paper/2205.07843/) (2022)
- [Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks](https://mlsanity.com/paper/2101.09833/) (2021)
- [Emerging trends in machine learning for computational fluid dynamics](https://mlsanity.com/paper/2211.15145/) (2022)
- [Reduced-order modeling for parameterized large-eddy simulations of atmospheric pollutant dispersion](https://mlsanity.com/paper/2208.01518/) (2022)

## Built on by (most cited first, 4 of 4)

- [SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.06286/) (2024)
- [Sequential learning based PINNs to overcome temporal domain complexities in unsteady flow past flapping wings](https://mlsanity.com/paper/2503.15679/) (2025)
- [Understanding the training of PINNs for unsteady flow past a plunging foil through the lens of input subdomain level loss function gradients](https://mlsanity.com/paper/2402.17346/) (2024)
- [Learning Fluid-Structure Interaction with Physics-Informed Machine Learning and Immersed Boundary Methods](https://mlsanity.com/paper/2505.18565/) (2025)

## Abstract (arXiv)

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady flows past moving bodies, such as flapping wings is scarce. Earlier studies mostly relied on transferring to a body attached frame of reference which is restrictive towards handling multiple moving bodies or deforming structures. Hence, in the present work, an immersed boundary aware framework has been explored for developing surrogate models for unsteady flows past moving bodies. Specifically, simultaneous pressure recovery and velocity reconstruction from Immersed boundary method (IBM) simulation data has been investigated. While, efficacy of velocity reconstruction has been tested against the fine resolution IBM data, as a step further, the pressure recovered was compared with that of an arbitrary Lagrange Eulerian (ALE) based solver. Under this framework, two PINN variants, (i) a moving-boundary-enabled standard Navier-Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss weighting conditions. MB-PINN is found to be superior to MB-IBM-PINN when it a priori knowledge of the solid body position and velocity are available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget.