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Article
Computer Science, Interdisciplinary Applications
Junyan He et al.
Summary: This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression. A combinatorial, key-based design system is proposed to generate different lattice designs, and the finite element method is used to simulate their response. The trained models accurately predict lattice energy absorption curves and can be extended to new designs via transfer learning.
COMPUTERS & STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Junyan He et al.
Summary: This paper investigates the application of graph convolutional networks in the deep energy method model for solving the momentum balance equation of linear elastic and hyperelastic materials in three-dimensional space. Numerical examples demonstrate that the proposed method achieves similar accuracy with shorter run time compared to traditional methods. The study also discusses two different spatial gradient computation techniques.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(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
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
Computer Science, Interdisciplinary Applications
Shantanu Shahane et al.
Summary: Surrogate neural network models are used in cell phone camera systems to accurately evaluate lens configurations and analyze optical properties. They provide efficient handling of large amounts of data for sensitivity and uncertainty analysis, and are valuable tools for optimizing tolerance design and component matching.
COMPUTERS & STRUCTURES
(2022)
Article
Mechanics
Diab W. Abueidda et al.
Summary: In this study, the potential energy formulation and deep learning are merged to introduce the deep energy method, which shows potential for solving deformation problems in hyperelastic and viscoelastic materials.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Computer Science, Artificial Intelligence
Khader M. Hamdia et al.
Summary: This study introduces a method to optimize the architecture and feature configurations of ML models using genetic algorithm. It validates the effectiveness of this approach through optimization in deep neural networks and adaptive neuro-fuzzy inference systems. The method has broad application potential in optimizing ML models in various complex systems.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Sina Amini Niaki et al.
Summary: The study introduces a Physics-Informed Neural Network (PINN) to simulate the thermal-chemical evolution of a composite material curing in an autoclave. By optimizing deep neural network (DNN) parameters using a physics-based loss function, the research solves coupled differential equations, designs a PINN with two disconnected subnetworks, and develops a sequential training algorithm. The approach incorporates explicit discontinuities at the composite-tool interface and enforces known physical behavior in the loss function to enhance solution accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(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
Sifan Wang et al.
Summary: PINNs show promise in integrating physical models with observational data, but struggle with high-frequency or multi-scale features. Through NTK theory, this work investigates the limitations of PINNs and proposes novel architectures to address these challenges.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Kevin Linka et al.
Summary: Constitutive artificial neural networks (CANNs) are a novel machine learning architecture for data-driven modeling of the mechanical constitutive behavior of materials. By incorporating information from stress-strain data, materials theory, and additional information, CANNs can efficiently learn the constitutive behavior of complex materials with minimal training data. The ability to predict properties of new materials without existing stress-strain data makes CANNs potentially useful for in-silico material design in the future.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
E. Fatehi et al.
Summary: The use of machine learning in designing architectured ceramics can improve efficiency and performance, resulting in increased frictional energy dissipation, reduced sliding distance, lowered strain energy, higher safety factor, and delayed structural failure.
MATERIALS & DESIGN
(2021)
Article
Thermodynamics
Shengze Cai et al.
Summary: Physics-informed neural networks (PINNs) have gained popularity in engineering fields for their effectiveness in solving realistic problems with noisy data and partially missing physics. Through automatic differentiation to evaluate differential operators and defining a multitask learning problem, PINNs have been applied to various heat transfer problems, bridging the gap between computational and experimental heat transfer.
JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME
(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
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
Engineering, Mechanical
Chengping Rao et al.
Summary: In this paper, a new method called Physics-Informed Neural Network (PINN) is introduced to model PDE solutions without using labeled data for computational mechanics problems. By taking displacement and stress components as DNN outputs inspired by hybrid finite element analysis, the accuracy and trainability of the network are significantly improved. A composite scheme based on multiple single DNNs is established to forcibly satisfy the initial/boundary conditions, overcoming issues related to weakly imposed conditions in traditional PINN frameworks.
JOURNAL OF ENGINEERING MECHANICS
(2021)
Article
Chemistry, Physical
Yongtae Kim et al.
Summary: In this study, a deep neural network-based forward design approach is proposed to efficiently search for superior materials beyond the domain of the initial training set by gradually updating the neural network with active transfer learning and data augmentation methods. This approach compensates for the weak predictive power of neural networks on unseen domains.
NPJ COMPUTATIONAL MATERIALS
(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)
Proceedings Paper
Computer Science, Artificial Intelligence
Rick Groenendijk et al.
Summary: This paper proposes a weighting scheme based on the coefficient of variations for single-task multi-loss problems, dynamically adjusting loss weights during training without additional optimization. Empirical results show the effectiveness of this approach on depth estimation and semantic segmentation tasks.
2021 IEEE WINTER CONFERENCE ON APPLICATIONS OF COMPUTER VISION (WACV 2021)
(2021)
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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
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(2018)
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(2013)
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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2009)
