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Article
Mathematics, Applied
Kazuo Yonekura et al.
Summary: This paper proposes a super-resolution method for finite element analysis that predicts a high-resolution stress tensor field from low-resolution contour plots using a neural network. The proposed method aims to obtain accurate results within limited resources and ensures physically reasonable solutions by minimizing the residual of equilibrium constraints. The network is trained and validated using finite element analysis results of simple and realistic shapes.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2023)
Article
Engineering, Biomedical
Ali Kamali et al.
Summary: Elasticity imaging is a technique to discover the mechanical properties of tissues using deformation and force measurements. We use physics-informed neural networks (PINN) to simultaneously discover the distribution of elastic modulus and Poisson's ratio in linear elasticity problems. Our model is validated through experiments and simulations.
ACTA BIOMATERIALIA
(2023)
Article
Mathematics, Interdisciplinary Applications
Jinshuai Bai et al.
Summary: In this paper, a modified loss function called LSWR loss function is proposed for the Physics-Informed Neural Network (PINN) in computational solid mechanics. Through testing and comparison in 2D and 3D problems, the effectiveness, robustness, and accuracy of the PINN based on the LSWR loss function in predicting displacement and stress fields are demonstrated.
COMPUTATIONAL MECHANICS
(2023)
Article
Automation & Control Systems
Zhiqiang Gong et al.
Summary: This paper develops a physics-informed convolutional neural network for the thermal simulation surrogate without labeled data. The finite difference method is used to integrate the heat conduction equation and loss function construction, guiding the surrogate model training. The experiments demonstrate that the proposed method can provide comparable predictions with numerical methods and data-driven deep learning models.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Mathematics, Applied
W. Wu et al.
Summary: Material identification is carried out using physics-informed neural networks (PINNs) to understand the relationship between mechanical properties and mechanical functions. Efficient strategies are developed to sample observational data and enforce boundary conditions. The proposed methods achieve accurate estimation of material parameters and have wide applications in structural integrity optimization and material development.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2023)
Article
Computer Science, Interdisciplinary Applications
Sifan Wang et al.
Summary: This work investigates the Neural Tangent Kernel (NTK) of Physics-informed neural networks (PINNs) and demonstrates that it can converge to a deterministic kernel that remains constant during training under appropriate conditions. A novel gradient descent algorithm is proposed to adaptively calibrate the convergence rate of total training error using the eigenvalues of NTK. A series of numerical experiments are conducted to validate the theory and practical effectiveness of the proposed algorithms.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Alexander Henkes et al.
Summary: Physics informed neural networks are a method used in applied mathematics and engineering to solve partial differential equations. However, due to their global approximation approach, they face challenges in displaying localized effects and strong nonlinear solution fields. To overcome these issues, researchers have studied adaptive training strategies and domain decomposition.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Chemistry, Physical
Vivek Oommen et al.
Summary: This study proposes a framework that combines a convolutional autoencoder with a deep neural operator to accelerate the prediction of microstructure evolution in materials and reduce computational costs.
NPJ COMPUTATIONAL MATERIALS
(2022)
Article
Engineering, Aerospace
Zeyu Cao et al.
Summary: This paper proposes a neural network model that combines multi-task learning and attention mechanism for thermal stress and deformation analysis of satellite motherboards. By incorporating physics knowledge and balancing the loss functions, the proposed model improves the prediction accuracy of multiple physics tasks, especially on small data sets.
Article
Computer Science, Interdisciplinary Applications
Han Gao et al.
Summary: The paper introduces a novel physics-constrained CNN learning architecture to learn solutions of parametric PDEs on irregular domains without labeled data. Elliptic coordinate mapping is used to enable coordinate transforms between irregular physical domain and regular reference domain. The proposed method has been assessed by solving a number of steady-state PDEs on irregular domains and has shown notable superiority over the FC-NN based PINN in terms of efficiency and accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Ehsan Haghighat et al.
Summary: This study presents the application of Physics Informed Neural Networks (PINN) in solid mechanics, improving accuracy and convergence with a multi-network model and Isogeometric Analysis. The study demonstrates the importance of honoring physics in improving robustness and highlights the potential application of PINN in sensitivity analysis and surrogate modeling.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Sifan Wang et al.
Summary: The study reviews recent advances in scientific machine learning, focusing specifically on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. It also proposes a learning rate annealing algorithm and a novel neural network architecture to address numerical stiffness issues in training constrained neural networks.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Multidisciplinary Sciences
Md Tauhidul Islam et al.
SCIENTIFIC REPORTS
(2020)
Article
Computer Science, Interdisciplinary Applications
Yinhao Zhu et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Review
Engineering, Biomedical
Karol Miller et al.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2019)
Article
Acoustics
Bonghun Shin et al.
ULTRASONIC IMAGING
(2016)
Article
Biophysics
Kaveh Laksari et al.
JOURNAL OF BIOMECHANICS
(2012)
Review
Engineering, Biomedical
M. M. Doyley
PHYSICS IN MEDICINE AND BIOLOGY
(2012)
Review
Biophysics
Simon Chatelin et al.
Article
Engineering, Biomedical
Paul E. Barbone et al.
PHYSICS IN MEDICINE AND BIOLOGY
(2007)
