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Chinese physics B 2024年第2期33卷 96-107页

作者：郭亚楠曹小群宋君强冷洪泽 College of Meteorology and Oceanography National University of Defense TechnologyChangsha 410073China College of Computer National University of Defense TechnologyChangsha 410073China Naval Aviation University Huludao 125001China

Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics *** recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential *** them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical *** the field of nonlinear science,solitary waves and rogue waves have been important research *** this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information *** addition,we employ meta-learning optimization to speed up the training *** apply the improved PINNs to the numerical simulation and prediction of solitary and rogue *** evaluate the accuracy of the prediction results by error *** experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.

关键词： physics-informed neural networks gradient-enhanced loss function meta-learned optimization nonlinear science

TCAS-PINN:physics-informed neural networks with a novel temporal causality-based adaptive sampling method

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Chinese physics B 2024年第5期33卷 344-364页

作者：郭嘉王海峰古仕林侯臣平 College of Science National University of Defense TechnologyChangsha 410073China

physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss *** performance of PINNs is generally affected by both training and ***,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are ***,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms *** is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling *** temporal knowledge into sampling remains to be *** fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal *** designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into *** experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the *** demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.

关键词： partial differential equation physics-informed neural networks residual-based adaptive sampling temporal causality

physics-informed neural networks for diffraction tomography

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Advanced Photonics 2022年第6期4卷 44-55页

作者： Amirhossein Saba Carlo Gigli Ahmed B.Ayoub Demetri Psaltis École Polytechnique Fédérale de Lausanne Optics LaboratoryLausanneSwitzerland

We propose a physics-informed neural network(PINN)as the forward model for tomographic reconstructions of biological *** demonstrate that by training this network with the Helmholtz equation as a physical loss,we can predict the scattered field *** will be shown that a pretrained network can be fine-tuned for different samples and used for solving the scattering problem much faster than other numerical *** evaluate our methodology with numerical and experimental *** PINNs can be generalized for any forward and inverse scattering problem.

关键词： deep learning physics-informed neural networks scattering three-dimensional imaging optical diffraction tomography

Meshfree-based physics-informed neural networks for the unsteady Oseen equations

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Chinese physics B 2023年第4期32卷 151-159页

作者：彭珂依岳靖张文李剑 School of Mathematics and Data Science Shaanxi University of Science and TechnologyXi’an 710021China School of Electrical and Control Engineering Shaanxi University of Science and TechnologyXi’an 710021China

We propose the meshfree-based physics-informed neural networks for solving the unsteady Oseen ***,based on the ideas of meshfree and small sample learning,we only randomly select a small number of spatiotemporal points to train the neural network instead of forming a ***,we optimize the neural network by minimizing the loss function to satisfy the differential operators,initial condition and boundary ***,we prove the convergence of the loss function and the convergence of the neural *** addition,the feasibility and effectiveness of the method are verified by the results of numerical experiments,and the theoretical derivation is verified by the relative error between the neural network solution and the analytical solution.

关键词： physics-informed neural networks the unsteady Oseen equation convergence small sample learning

Solving nonlinear soliton equations using improved physics-informed neural networks with adaptive mechanisms

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Communications in Theoretical physics 2023年第9期75卷 36-50页

作者： Yanan Guo Xiaoqun Cao Kecheng Peng Simulation and Training Center Naval Aviation UniversityHuludao 125001China College of Computer National University of Defense TechnologyChangsha 410073China College of Meteorology and Oceanography National University of Defense TechnologyChangsha 410073China

Partial differential equations(PDEs)are important tools for scientific research and are widely used in various ***,it is usually very difficult to obtain accurate analytical solutions of PDEs,and numerical methods to solve PDEs are often computationally intensive and very *** recent years,physics informed neural networks(PINNs)have been successfully applied to find numerical solutions of PDEs and have shown great *** the while,solitary waves have been of great interest to researchers in the field of nonlinear *** this paper,we perform numerical simulations of solitary wave solutions of several PDEs using improved *** improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results,which is important for physical field simulations,in addition,an adaptive activation function is *** introducing hyperparameters in the activation function to change the slope of the activation function to avoid the disappearance of the gradient,computing time is saved thereby speeding up *** this paper,the m Kd V equation,the improved Boussinesq equation,the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and the p-g BKP equation are selected for study,and the errors of the simulation results are analyzed to assess the accuracy of the predicted solitary wave *** experimental results show that the improved PINNs are significantly better than the traditional PINNs with shorter training time but more accurate prediction *** improved PINNs improve the training speed by more than 1.5 times compared with the traditional PINNs,while maintaining the prediction error less than 10~(-2)in this order of magnitude.

关键词： physics-informed neural networks adaptive activation function partial differential equations solitary wave

Non-Fourier Heat Conduction based on Self-Adaptive Weight physics-informed neural networks

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Non-Fourier Heat Conduction based on Self-Adaptive Weight Ph...

physics-informed deep learning for fringe pattern analysis

第40届中国控制会议

作者： Shuyan Shi Ding Liu Zhongdan Zhao National & Local Joint Engineering Research Center of Crystal Growth Equipment and System Integration Xi'an University of Technology Shananxi Key Laboratory of Complex System Control and Intelligent Information Processing

This paper establishes the non-Fourier heat conduction model to describe the heat transfer process of mono-crystalline silicon under the condition of unstable thermal field and thermal shock in the Czochralski method.A novel differential equations solver called physics-informed neural networks（PINN） algorithm was *** with finite element method（FEM）,this method has some advantages like no grid requirement and easily *** order to deal with the unbalance of constraint condition and speed up the convergence,we propose a novel method called Self-Adaptive Weight physics-informed neural networks（SWPINN）.The comparison of the experimental results of SWPINN and COMSOL verifies the effectiveness of *** modifying the parameter of non-Fourier heat conduction model,this paper obtains the temperature distribution under different heat relaxation ***,comparison between SWPINN and PINN shows that the proposed method has faster convergence speed and higher accuracy.

关键词： Non-Fourier Heat Conduction physics-informed neural networks Partial Differential Equation Monocrystalline Silicon Czochralski Method

来源： cnki会议评论

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Opto-Electronic Advances 2024年第1期7卷 4-15页

作者： Wei Yin Yuxuan Che Xinsheng Li Mingyu Li Yan Hu Shijie Feng Edmund Y.Lam Qian Chen Chao Zuo Smart Computational Imaging Laboratory(SCILab) School of Electronic and Optical EngineeringNanjing University of Science and TechnologyNanjing 210094China Smart Computational Imaging Research Institute(SCIRI)of Nanjing University of Science and Technology Nanjing 210019China Jiangsu Key Laboratory of Spectral Imaging&Intelligent Sense Nanjing 210094China Department of Electrical and Electronic Engineering The University of Hong KongPokfulamHong Kong SAR 999077China

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical *** neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe ***,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning *** this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) *** parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning *** by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end *** results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during *** proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

关键词： optical metrology deep learning physics-informed neural networks fringe analysis phase retrieval

A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant networks

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Journal of Systems Science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun DONG Huanhe FANG Yong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Multi-head neural networks for simulating particle breakage dynamics

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 130-141页

作者： Abhishek Gupta Barada Kanta Mishra School of Mechanical Sciences Indian Institute of Technology(IIT)GoaPonda 403401India School of Chemical and Materials Science Indian Institute of Technology(IIT)GoaPonda 403401India

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential *** this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing *** conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model *** network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle *** method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding *** agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

关键词： Particle breakage dynamics Population balance equation physics-informed neural networks

Multi-Scale-Matching neural networks for thin plate bending problem

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Theoretical & Applied Mechanics Letters 2024年第1期14卷 11-15页

作者： Lei Zhang Guowei He The State Key Laboratory of Nonlinear Mechanics Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of Engineering Science University of Chinese Academy of SciencesBeijing 100049China

physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation *** resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation *** by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,***,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region *** results for the thin plate problem validate the proposed method.

关键词： Singular perturbation physics-informed neural networks Boundary layer Machine learning