Article
Computer Science, Interdisciplinary Applications
Simone Rodini
Summary: The study presents a simple recursive algorithm for computing the first-and second-order derivatives with respect to the inputs of a deep feed forward neural network, incorporating derivatives with respect to network parameters. The algorithm is tested in the context of quantum mechanical variational problems for simple potentials, modeling ground-state wave function using a DFNN.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mathematics
Yuting Yang, Gang Mei
Summary: In this study, a deep learning-based approach was proposed for the numerical investigation of soil-water vertical infiltration, and a comprehensive evaluation and analysis of the soil-water infiltration process in different soil types was performed. The results showed that the proposed approach had a smaller error and could obtain more accurate numerical results compared to the traditional numerical method. Additionally, it was found that medium-loam soils were less susceptible to water infiltration and were more suitable for filling artificial slopes and dams. This approach can be used for slope stability assessment under rainfall conditions and for slope stabilization measures.
Article
Engineering, Mechanical
Chuang Liu, HengAn Wu
Summary: We propose a novel approach for solving scientific problems governed by differential equations using physics-informed neural networks (PINNs). This method evaluates the residuals of equations on subdomains of the computational zone through numerical integration. Test functions and integral weights are embedded within convolutional filters to extract information from these residuals. Our approach demonstrates exceptional parallel abilities when dealing with large numbers of sub-domains, and is more efficient than variational physics-informed neural networks with domain decomposition (hp-VPINNs). It offers tremendous potential for solving problems with complex geometries or nonlinearities.
EXTREME MECHANICS LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Lei Yuan, Yi-Qing Ni, Xiang-Yun Deng, Shuo Hao
Summary: Physics informed neural networks (PINNs) are a novel deep learning paradigm for solving forward and inverse problems of nonlinear partial differential equations (PDEs). This study proposes an auxiliary PINN (A-PINN) framework that bypasses the limitation of integral discretization by defining auxiliary output variables and using automatic differentiation. The A-PINN demonstrates higher accuracy compared to traditional PINN and shows good performance in solving various nonlinear IDE problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Chemistry, Multidisciplinary
Perizat Omarova, Yedilkhan Amirgaliyev, Ainur Kozbakova, Aisulyu Ataniyazova
Summary: This article proposes an innovative method for studying river channel pollution using advanced neural network techniques and numerical simulations. The method offers advantages in terms of accuracy and computational efficiency, providing essential information for decision-makers and environmental stakeholders.
APPLIED SCIENCES-BASEL
(2023)
Article
Multidisciplinary Sciences
Jieting Chen, Chao Qian, Jie Zhang, Yuetian Jia, Hongsheng Chen
Summary: The authors propose a generation-elimination framework that accurately forecasts inaccessible spectra by correlating spectra from different frequency bands without consulting structural information. This framework accelerates the unification of metasurface designs and enables versatile applications involving cross-wavelength information correlation. The study also introduces a dimensionality reduction approach to visualize the abstract correlated spectra data encoded in latent spaces.
NATURE COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Jie Long, A. Q. M. Khaliq, K. M. Furati
Summary: This paper employs a variant of physics-informed neural network to identify time-varying parameters of the COVID-19 transmission model, and uses Long Short-Term Memory neural network to predict future parameter changes. The accuracy and effectiveness of parameter learning are validated through computing model solutions and effective reproduction numbers. The numerical simulations show that the combination of PINN and LSTM produces accurate and effective results.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Mathematics
Kaixuan Shao, Yinghan Wu, Suizi Jia
Summary: The research on free surface flow in fluid mechanics focuses on tracking and describing the motion of free surfaces. The Neural Particle Method (NPM) is a meshless approach for solving incompressible free surface flow that has shown effectiveness but faces challenges in more complex scenarios. In this paper, an improved Neural Particle Method (INPM) is proposed, which incorporates alpha-shape technology to track and recognize the fluid boundary and updates boundary conditions constantly. Through numerical examples, it is demonstrated that INPM accurately tracks and recognizes the fluid boundary, even in situations with uneven particle distribution, offering a better solution for complex free surface flow problems.
Article
Optics
Md Sadman Sakib Rahman, Jingxi Li, Deniz Mengu, Yair Rivenson, Aydogan Ozcan
Summary: Researchers in the USA have made significant improvements in the performance of diffractive optical networks, signaling a major advancement in their use for optics-based computation and machine learning. By utilizing feature engineering and ensemble learning, they were able to substantially enhance the statistical inference capabilities of these networks.
LIGHT-SCIENCE & APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yuekun Yang, Youssef Mesri
Summary: The Physical Informed Neural Networks (PINN) model is a promising deep learning approach for predicting physical phenomena governed by PDEs, especially for improving the accuracy of mass transfer problem predictions. However, it is sensitive to input dataset accuracy and struggles with predicting phenomena in complex geometries. In this article, the use of the PINN model is improved by combining it with a One-hot matrix model to better account for boundary conditions in complex geometries. The use of non-uniform weights from physics, such as the Q-criterion, is also investigated. The proposed model accurately predicts two-dimensional flows around sharp rectangular obstacles from low-resolution datasets.
COMPUTERS & FLUIDS
(2022)
Article
Computer Science, Artificial Intelligence
Muhammad Izzatullah, Isa Eren Yildirim, Umair Bin Waheed, Tariq Alkhalifah
Summary: This paper introduces a PINN-based inversion framework called HypoPINN for automatic hypocenter localization and proposes an approximate Bayesian framework for estimating its predictive uncertainties. The effectiveness of this method is demonstrated through numerical examples.
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
(2022)
Article
Neurosciences
Lukas Fischer, Raul Mojica Soto-Albors, Vincent D. Tang, Brendan Bicknell, Christine Grienberger, Valerio Francioni, Richard Noud, Lucy M. Palmer, Naoya Takahashi
Summary: Dendrites receive and process input signals from neurons, playing a crucial role in brain function. Recent research using new experimental and computational technologies has revealed the importance of dendrites in brain work and provided new theoretical insights. Studies have found that dendrites actively mediate sensory perception and learning, contributing to our understanding of both biological and artificial neural computation.
JOURNAL OF NEUROSCIENCE
(2022)
Article
Computer Science, Interdisciplinary Applications
Mahdad Eghbalian, Mehdi Pouragha, Richard Wan
Summary: In this work, a deep neural network architecture called Elasto-Plastic Neural Network (EPNN) is proposed to efficiently surrogate classical elasto-plastic constitutive relations. The EPNN incorporates physics aspects of classical elasto-plasticity, allowing for more efficient training with less data and better extrapolation capability. The architecture is model and material-independent and can be adapted to a wide range of elasto-plastic materials. The superiority of EPNN is demonstrated through predicting strain-controlled loading paths for sands with different initial densities.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Mechanics
Mustafa Z. Yousif, Linqi Yu, Hee-Chang Lim
Summary: This study presents a deep learning-based framework that utilizes the concept of generative adversarial networks to recover high-resolution turbulent velocity fields from extremely low-resolution data. The model, a multiscale enhanced super-resolution generative adversarial network, accurately reconstructs high-resolution velocity fields, as demonstrated by evaluating its performance using direct numerical simulation data. The results show that the model is capable of reconstructing high-resolution velocity fields at different down-sampling factors and within the range of the training Reynolds numbers.
Article
Mathematics, Applied
Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, Francesco Piccialli
Summary: Physics-Informed Neural Networks (PINN) are a type of neural network that incorporates model equations, such as partial differential equations, as a component. PINNs have been used to solve various types of equations, including fractional equations and stochastic partial differential equations. Current research focuses on optimizing PINN through different aspects, such as activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the demonstrated feasibility of PINN in certain cases compared to traditional numerical techniques, there are still unresolved theoretical issues.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Ehsan Haghighat, Maziar Raissi, Adrian Moure, Hector Gomez, Ruben Juanes
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
Sina Amini Niaki, Ehsan Haghighat, Trevor Campbell, Anoush Poursartip, Reza Vaziri
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
Ehsan Haghighat, Ali Can Bekar, Erdogan Madenci, Ruben Juanes
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
Umair bin Waheed, Ehsan Haghighat, Tariq Alkhalifah, Chao Song, Qi Hao
Summary: The proposed algorithm based on physics-informed neural networks offers a high traveltime accuracy for a wide range of applications in seismology. It leverages machine learning techniques like transfer learning and surrogate modeling to speed up computations for updated velocity models and source locations. The method's flexibility in incorporating various physical properties and improving convergence rate makes it an efficient forward modeling engine for seismological applications.
COMPUTERS & GEOSCIENCES
(2021)
Article
Mechanics
K. Koocheki, S. Pietruszczak, E. Haghighat
Summary: In this study, a computational framework is proposed to model the mechanical response of structural masonry at both meso and macroscale. The framework can adequately predict the load-deformation response and fracture pattern of masonry. An anisotropy parameter is introduced in the macroscale approach, and the material parameters are identified using "virtual data" generated from mesoscale analysis.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Engineering, Mechanical
Mohammad Vahab, Ehsan Haghighat, Maryam Khaleghi, Nasser Khalili
Summary: We explore the application of Physics-Informed Neural Networks (PINNs) with Airy stress functions and Fourier series in finding optimal solutions to reference biharmonic problems in elasticity and elastic plate theory. Our work demonstrates a novel application of classical analytical methods in constructing efficient neural networks with minimal parameters, which are accurate and fast in evaluation. We find that enriching the feature space with Airy stress functions can significantly improve the accuracy of PINN solutions for biharmonic PDEs.
JOURNAL OF ENGINEERING MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Ali Can Bekar, Erdogan Madenci, Ehsan Haghighat
Summary: This study introduces a generalized upwind scheme called directional nonlocality for the numerical solution of linear and nonlinear hyperbolic PDEs. By introducing an internal length parameter and a weight function, this method achieves stable discretization of hyperbolic PDEs and constructs solutions that compare well with analytical/reference solutions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Ehsan Haghighat, Danial Amini, Ruben Juanes
Summary: This paper presents a physics-informed neural network (PINN) approach for solving the equations of coupled flow and deformation in porous media. Incorporating multiple differential relations into the loss function can lead to an unstable optimization problem due to the dynamics of the problem. A dimensionless form of the coupled governing equations is proposed, and a sequential training approach based on stress-split algorithms is introduced.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Mengwu Guo, Ehsan Haghighat
Summary: An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. The error bound is formulated as the constitutive relation error defined by the solution pair. It provides an upper bound of the global error of neural network discretization and studies the bounding property and asymptotic behavior of the physics-informed neural network solutions.
JOURNAL OF ENGINEERING MECHANICS
(2022)
Article
Engineering, Mechanical
Danial Amini, Ehsan Haghighat, Rubn Juanes
Summary: This study investigates the application of physics-informed neural networks (PINNs) to the forward solution of thermo-hydro-mechanical (THM) problems in porous media. To address the challenges of multiphysics problems, the researchers propose dimensionless governing equations, a sequential training strategy, and adaptive weight strategies.
JOURNAL OF ENGINEERING MECHANICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ehsan Haghighat, David Santillan
Summary: We introduce a phase-field model that utilizes the deviatoric stress decomposition to represent shear fractures. This approach allows us to incorporate the general three-dimensional Mohr-Coulomb failure function for establishing relationships and evaluating peak and residual stresses. Our model demonstrates impressive performance in several benchmark problems involving shear fracture and strain localization. It successfully captures the conjugate failure modes during biaxial compression tests and addresses the challenging slope stability problem faced by most geomechanics models.
COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Arda Mavi, Ali Can Bekar, Ehsan Haghighat, Erdogan Madenci
Summary: This study proposes a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). It employs the nonlocal Peridynamic Differential Operator (PDDO) as a convolutional filter to evaluate derivatives of the field variable. The NN captures time dynamics in a smaller latent space through encoder-decoder layers with a modified Convolutional Long-short Term Memory (ConvLSTM) layer.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Automation & Control Systems
Ehsan Haghighat, Sahar Abouali, Reza Vaziri
Summary: Constitutive models are fundamental in modeling physical processes by connecting conservation laws with system kinematics. However, characterizing these models can be challenging, especially in nonlinear regimes. We believe that theory-based parametric elastoplastic models are still the most efficient and predictive.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Mechanics
M. Vahab, B. Shahbodagh, E. Haghighat, N. Khalili
Summary: This paper presents the application of Physics-Informed Neural Networks (PINNs) in the forward and inverse analysis of pile-soil interaction problems. The main challenge in the Artificial Neural Network (ANN) modeling of such interaction is the abrupt changes in material properties that cause discontinuities in displacement solution gradient. To address this, a domain-decomposition multi-network model is proposed to handle the strain field discontinuities at common boundaries of pile-soil regions and soil layers. The model is demonstrated on the analysis and parametric study of single piles embedded in homogeneous and layered formations, under axisymmetric and plane strain conditions. The performance of the model in inverse analysis of pile-soil interaction is particularly investigated, showing successful inversion of soil parameters in layered formations using localized data obtained via fiber optic strain sensing along the pile length.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)