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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
Computer Science, Interdisciplinary Applications
Jan N. Fuhg et al.
Summary: This paper introduces the research status of deep neural networks as universal approximators of PDEs and compares the advantages and disadvantages of two different methods. An improved deep energy method is proposed to solve the fine features in solid mechanics and a numerical integration scheme is introduced to enhance the flexibility of the method.
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
Engineering, Multidisciplinary
Jinshuai Bai et al.
Summary: The Neural Particle Method (NPM) is a newly proposed meshfree method for hydrodynamics modeling based on Physics-Informed Neural Network (PINN). In this study, a general NPM (gNPM) has been developed to address viscous hydrodynamics modeling, providing improved computational efficiency. By considering the viscous term in the conservation of momentum, the effectiveness and robustness of gNPM have been demonstrated through several benchmark cases, showing its ability to handle uneven particle distributions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Jon A. Rivera et al.
Summary: Neural networks are widely used for solving partial differential equations and require numerical integration to approximate definite integrals. This study illustrates potential quadrature problems in these applications through 1D numerical examples and proposes alternative integration schemes such as Monte Carlo methods, adaptive integration, polynomial approximations, and regularization terms. The choice of integration method depends on the dimensionality of the problem.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Somdatta Goswami et al.
Summary: This study proposes a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis. By incorporating physics laws and labeled data in training, V-DeepONet accurately predicts key quantities in brittle fracture and has wide application potential.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Artificial Intelligence
Zixue Xiang et al.
Summary: The paper introduces a method of defining the loss function through adaptive weights and demonstrates that the self-adaptive loss balanced physics-informed neural networks (lbPINNs) outperform PINNs in solving partial differential equations.
Article
Engineering, Chemical
C. P. Batuwatta-Gamage et al.
Summary: This paper presents a Physics-Informed Neural Network-based surrogate framework for coupling moisture concentration and shrinkage of a plant cell during drying. The results show that the PINN-based model outperforms regular deep neural networks in terms of accuracy and stability when predicting moisture concentration and shrinkage, making it a powerful tool for investigating complex drying mechanisms.
JOURNAL OF FOOD ENGINEERING
(2022)
Review
Engineering, Mechanical
Shengze Cai et al.
Summary: Significant progress has been made in simulating flow problems over the last 50 years, but challenges remain in incorporating noisy data, complex mesh generation, and solving high-dimensional problems. Physics-informed neural networks (PINNs) have been demonstrated as effective in solving inverse flow problems related to various fluid dynamics scenarios.
ACTA MECHANICA SINICA
(2021)
Article
Mechanics
Xiaoying Zhuang et al.
Summary: This paper introduces a Deep Autoencoder based Energy Method (DAEM) for the bending, vibration, and buckling analysis of Kirchhoff plates. The DAEM utilizes higher-order continuity, integrates a deep autoencoder and the minimum total potential principle, and serves as an unsupervised feature learning method. It efficiently identifies patterns, minimizes total potential energy, extracts fundamental frequencies and critical buckling loads, alleviates gradient problems, and improves computational efficiency and generality through transfer learning.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Engineering, Multidisciplinary
Vien Minh Nguyen-Thanh et al.
Summary: The Parametric Deep Energy Method (P-DEM) presented in this work solves elasticity problems considering strain gradient effects using physics-informed neural networks (PINNs). It does not require classical discretization and simplifies implementation by defining potential energy. Normalized inputs in a parametric/reference space prevent vanishing gradients and enable faster convergence. The method utilizes NURBS basis functions for forward-backward mapping and Gauss quadrature for approximating total potential energy in the loss function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Ehsan Haghighat et al.
Summary: The Physics-Informed Neural Network (PINN) framework combines physics with deep learning to solve PDEs and identify parameters. A nonlocal PINN approach with long-range interactions shows superior performance in solution accuracy and parameter inference compared to local approaches.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Xiaowei Jin et al.
Summary: In the past 50 years, significant progress has been made in solving Navier-Stokes equations using various numerical methods, but challenges still exist in incorporating multi-fidelity data seamlessly and mesh generation for complex industrial applications. Physics-informed neural networks (PINNs) are employed to directly encode governing equations into deep neural networks, overcoming some limitations for simulating incompressible laminar and turbulent flows. The Navier-Stokes flow nets (NSFnets) are developed using velocity-pressure (VP) and vorticity-velocity (VV) formulations, showing promise in accuracy and convergence rate for benchmark problems as well as turbulent channel flows.
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
Engineering, Multidisciplinary
Wei Li et al.
Summary: This study establishes a neural network-based computational framework to characterize the finite deformation of elastic plates by incorporating known physical laws into the training process, reducing the data demand significantly. The accuracy of the modeling framework is carefully examined by applying it to different loading cases, showing satisfactory results with proper training strategies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Diab W. Abueidda et al.
Summary: Deep learning and the collocation method are merged to solve partial differential equations describing structures' deformation, offering a meshfree approach that avoids spatial discretization and data generation bottlenecks.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN 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)
Review
Computer Science, Theory & Methods
Laith Alzubaidi et al.
Summary: Deep learning has become the gold standard in the machine learning community, widely used in various domains and capable of learning massive data. Through a comprehensive survey, a better understanding of the most important aspects of deep learning is provided.
JOURNAL OF BIG DATA
(2021)
Article
Engineering, Multidisciplinary
Luning Sun et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Biochemical Research Methods
Pauli Virtanen et al.
Article
Engineering, Multidisciplinary
E. Samaniego et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Mechanical
Somdatta Goswami et al.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2020)
Article
Engineering, Multidisciplinary
Henning Wessels et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Computer Science, Interdisciplinary Applications
M. Raissi et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Engineering, Mechanical
Dehao Liu et al.
JOURNAL OF MECHANICAL DESIGN
(2019)
Article
Computer Science, Information Systems
Hongwei Guo et al.
CMC-COMPUTERS MATERIALS & CONTINUA
(2019)
Article
Computer Science, Interdisciplinary Applications
Justin Sirignano et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Review
Multidisciplinary Sciences
Yann LeCun et al.
Review
Computer Science, Artificial Intelligence
Juergen Schmidhuber
Article
Computer Science, Software Engineering
Jose Luis Morales et al.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2011)
