A general Neural Particle Method for hydrodynamics modeling

Bai, Jinshuai; Zhou, Ying; Ma, Ying; Jeong, Hyogu; Zhan, Haifei; Rathnayaka, C. M.; Sauret, Emilie; Gu, Yuantong

doi:10.1016/j.cma.2022.114740

Cited by 25 publications

(5 citation statements)

References 57 publications

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“…The q +1 predictions ûn i , ûn q+1 of ûn have to match the initial conditions u M n , where the mean squared error is used as a loss function to learn all stages û. The approach has been applied to fluid mechanics [329,330].…”

Section: Physics-informed Neural Networkmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning—instead, the primary audience is researchers on the verge of entering this field or those attempting to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

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Section: Physics-informed Neural Networkmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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“…PINNs have been widely used in problems where only insufficient data are available and the unknown systems are governed by known physics laws in terms of equations [479,[483][484][485][486]. As aforementioned, the physics laws are effective for specific problems.…”

Section: Physics-informed Neural Network (Pinn)mentioning

confidence: 99%

A survey on deep learning tools dealing with data scarcity: definitions, challenges, solutions, tips, and applications

et al. 2023

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Data scarcity is a major challenge when training deep learning (DL) models. DL demands a large amount of data to achieve exceptional performance. Unfortunately, many applications have small or inadequate data to train DL frameworks. Usually, manual labeling is needed to provide labeled data, which typically involves human annotators with a vast background of knowledge. This annotation process is costly, time-consuming, and error-prone. Usually, every DL framework is fed by a significant amount of labeled data to automatically learn representations. Ultimately, a larger amount of data would generate a better DL model and its performance is also application dependent. This issue is the main barrier for many applications dismissing the use of DL. Having sufficient data is the first step toward any successful and trustworthy DL application. This paper presents a holistic survey on state-of-the-art techniques to deal with training DL models to overcome three challenges including small, imbalanced datasets, and lack of generalization. This survey starts by listing the learning techniques. Next, the types of DL architectures are introduced. After that, state-of-the-art solutions to address the issue of lack of training data are listed, such as Transfer Learning (TL), Self-Supervised Learning (SSL), Generative Adversarial Networks (GANs), Model Architecture (MA), Physics-Informed Neural Network (PINN), and Deep Synthetic Minority Oversampling Technique (DeepSMOTE). Then, these solutions were followed by some related tips about data acquisition needed prior to training purposes, as well as recommendations for ensuring the trustworthiness of the training dataset. The survey ends with a list of applications that suffer from data scarcity, several alternatives are proposed in order to generate more data in each application including Electromagnetic Imaging (EMI), Civil Structural Health Monitoring, Medical imaging, Meteorology, Wireless Communications, Fluid Mechanics, Microelectromechanical system, and Cybersecurity. To the best of the authors’ knowledge, this is the first review that offers a comprehensive overview on strategies to tackle data scarcity in DL.

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“…Here, a stepwise PINN framework is proposed to deal with the large deformation of hypoelastic materials under the incremental computational framework. Different from other stepwise neural network techniques with physics‐informed models such as neural particle method 37 and general neural particle method, 18 the incremental advancement was implemented in the sPINN to solve path dependent hypoelastic finite deformation problems.…”

Section: Computational Implementations Of Spinnmentioning

confidence: 99%

“…PINN has been successfully applied to solve various hydrodynamic problems. 10,[14][15][16][17][18][19] Generally, PINN has the following advantages: (1) PINN is a meshless method, which discretizes the computing domain by collocating training points; (2) PINN can seamlessly integrate experimental data and physical laws; (3) PINN can be successfully trained with small or noisy data sets; and (4) PINN is easy to implement and solve inversion problems. Inspired by its superior performance, many researchers tried to introduce PINN into the field of solid mechanics.…”

Section: Introductionmentioning

confidence: 99%

A stepwise physics‐informed neural network for solving large deformation problems of hypoelastic materials

Luo

Wang

Lü

2023

Numerical Meth Engineering

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Physics‐informed neural network (PINN) has been widely concerned for its higher computational accuracy compared with conventional neural network. The merit of PINN mainly comes from its ability to embed known physical laws or equations into data‐based neural networks. However, when dealing with the rate‐dependent nonlinear problems, such as elasto‐plasticity with loading and unloading and hypoelastic large deformation, the conventional PINN cannot obtain satisfactory results. In this article, a stepwise physics‐informed neural network (sPINN) is proposed to solve large deformation problems of hypoelastic materials. The whole process of sPINN can be divided into a series of time steps. In each time step, the rate constitutive equation expressed by Hughes‐Winget algorithm and momentum governing equation are incorporated into the loss function as physical constraints. The displacement and stress fields can be resolved by completing the training process of each time step. Three numerical examples are designed to validate the proposed method by comparing with the solutions of FEM. The results show that sPINN can accurately resolve the displacement and stress fields in path‐dependent large deformation problems. Furthermore, the performance of the sPINN on small data sets are also discussed, which illustrates that sPINN is more capable of predicting the global solution on small data sets as compared with conventional artificial neural network.

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A general Neural Particle Method for hydrodynamics modeling

Cited by 25 publications

References 57 publications

Deep learning in computational mechanics: a review

Deep learning in computational mechanics: a review

A survey on deep learning tools dealing with data scarcity: definitions, challenges, solutions, tips, and applications

A stepwise physics‐informed neural network for solving large deformation problems of hypoelastic materials

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