A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network

Huang, Yi; Zhang, Zhiyu; Zhang, Xing

doi:10.3390/fluids7020056

Cited by 10 publications

(3 citation statements)

References 37 publications

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“…As a remedy, loss-specific weighting factors could be considered. Another potential solution is hard boundary constraint enforcement [7,8] or the direct-forcing immersed boundary method [29].…”

Section: Discussionmentioning

confidence: 99%

Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow

Pioch¹,

Harmening²,

Müller³

et al. 2023

Fluids

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Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-ω model, the mixing length model, an equation-free νt and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.

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Section: Discussionmentioning

confidence: 99%

Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow

Pioch¹,

Harmening²,

Müller³

et al. 2023

Fluids

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“…The advantages of the PINN are its ability to learn from small, limited training data and its interpretability, because it is informed by physical laws and is not purely data-driven [35]. PINNs can generalize well and find patterns even with limited data [36][37][38]. A deep learning model that combines physical laws and data performs better than some conventional numerical models using data assimilation [39].…”

Section: Artificial Neural Network and Physics-informed Neural Networkmentioning

confidence: 99%

Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Hu,

Kabala

2023

Atmosphere

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Interactions between clouds, aerosol, and precipitation are crucial aspects of weather and climate. The simple Koren–Feingold conceptual model is important for providing deeper insight into the complex aerosol–cloud–precipitation system. Recently, artificial neural networks (ANNs) and physics-informed neural networks (PINNs) have been used to study multiple dynamic systems. However, the Koren–Feingold model for aerosol–cloud–precipitation interactions has not yet been studied with either ANNs or PINNs. It is challenging for pure data-driven models, such as ANNs, to accurately predict and reconstruct time series in a small data regime. The pure data-driven approach results in the ANN becoming a “black box” that limits physical interpretability. We demonstrate how these challenges can be overcome by combining a simple ANN with physical laws into a PINN model (not purely data-driven, good for the small data regime, and interpretable). This paper is the first to use PINNs to learn about the original and modified Koren–Feingold models in a small data regime, including external forcings such as wildfire-induced aerosols or the diurnal cycle of clouds. By adding external forcing, we investigate the effects of environmental phenomena on the aerosol–cloud–precipitation system. In addition to predicting the system’s future, we also use PINN to reconstruct the system’s past: a nontrivial task because of time delay. So far, most research has focused on using PINNs to predict the future of dynamic systems. We demonstrate the PINN’s ability to reconstruct the past with limited data for a dynamic system with nonlinear delayed differential equations, such as the Koren–Feingold model, which remains underexplored in the literature. The main reason that this is possible is that the model is non-diffusive. We also demonstrate for the first time that PINNs have significant advantages over traditional ANNs in predicting the future and reconstructing the past of the original and modified Koren–Feingold models containing external forcings in the small data regime. We also show that the accuracy of the PINN is not sensitive to the value of the regularization factor (λ), a key parameter for the PINN that controls the weight for the physics loss relative to the data loss, for a broad range (from λ=1×103 to λ=1×105).

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“…In [22], the impact of the parameter on the learning rate is assessed, and a fixed value is used to obtain the final solution. Authors of [23] examines the effect of weight on both the loss function and its individual components by comparing their values for the resulting network. In [24], the approximate solutions obtained for different values of the weight parameter are compared with the exact solution.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary PINN Learning Algorithms Inspired by Approximation to Pareto Front for Solving Ill-Posed Problems

Lazovskaya,

Tarkhov,

Chistyakova

et al. 2023

Computation

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The article presents the development of new physics-informed evolutionary neural network learning algorithms. These algorithms aim to address the challenges of ill-posed problems by constructing a population close to the Pareto front. The study focuses on comparing the algorithm’s capabilities based on three quality criteria of solutions. To evaluate the algorithms’ performance, two benchmark problems have been used. The first involved solving the Laplace equation in square regions with discontinuous boundary conditions. The second problem considered the absence of boundary conditions but with the presence of measurements. Additionally, the study investigates the influence of hyperparameters on the final results. Comparisons have been made between the proposed algorithms and standard algorithms for constructing neural networks based on physics (commonly referred to as vanilla’s algorithms). The results demonstrate the advantage of the proposed algorithms in achieving better performance when solving incorrectly posed problems. Furthermore, the proposed algorithms have the ability to identify specific solutions with the desired smoothness.

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A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network

Cited by 10 publications

References 37 publications

Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow

Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow

Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Evolutionary PINN Learning Algorithms Inspired by Approximation to Pareto Front for Solving Ill-Posed Problems

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