Article
Engineering, Multidisciplinary
Alexander Henkes, Henning Wessels, Rolf Mahnken
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
Mechanics
R. Laubscher
Summary: In this study, single- and segregated-network physics-informed neural network (PINN) architectures were applied to predict momentum, species, and temperature distributions in a dry air humidification problem. It was found that the segregated-network PINN approach resulted in significantly lower losses compared to the single-network PINN architecture, showcasing the importance of segregated approach. The PINN models produced accurate results for temperature and velocity profiles, but there is still room for improvement in the species mass fraction predictions.
Article
Engineering, Multidisciplinary
Nilgun Guler Bayazit
Summary: This paper introduces a two-stage physics informed neural network, which significantly improves the prediction accuracy of PDE solutions by training each stage separately and not backpropagating the gradients to the first stage.
ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH
(2023)
Article
Biochemistry & Molecular Biology
Sara Ibrahim Omar, Chen Keasar, Ariel J. Ben-Sasson, Eldad Haber
Summary: The inverse protein folding problem seeks to predict an amino acid sequence that folds into a specific structure and performs a specific function. Machine learning techniques have been successful in generating functional sequences, but lack interoperability and robustness for proteins that function under non-ambient conditions. To address this, we propose a new Physics-Informed Neural Networks (PINNs)-based protein sequence design approach that combines molecular dynamics simulations and relaxation of binary programming. Our design framework demonstrates effectiveness in designing proteins that can function under non-ambient conditions.
Article
Mechanics
Mario De Florio, Enrico Schiassi, Barry D. Ganapol, Roberto Furfaro
Summary: This study accurately solves a thermal creep flow problem in a plane channel using Physics-Informed Neural Networks. By developing a specific framework that utilizes Constrained Expressions based on the Theory of Functional Connections, the study demonstrates that accurate solutions can be achieved with fast training times using shallow neural networks, such as Chebyshev NN and Legendre NN. The results show that the approach is effective in matching benchmarks and providing accurate solutions.
Article
Engineering, Multidisciplinary
Kevin Linka, Amelie Schafer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl
Summary: Understanding real-world dynamical phenomena is challenging, and machine learning has become the go-to technology for analyzing and making decisions based on these phenomena. However, traditional neural networks often ignore the fundamental laws of physics and fail to make accurate predictions. In this study, the combination of neural networks, physics informed modeling, and Bayesian inference is used to integrate data, physics, and uncertainties, improving the predictive potential of neural network models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Review
Engineering, Electrical & Electronic
Bin Huang, Jianhui Wang
Summary: The advances of deep learning techniques have brought new opportunities to power systems. However, there are challenges in applying deep learning in power systems, such as the requirement for high-quality training data, production of physically inconsistent solutions, and low interpretability. Physics-informed neural networks (PINNs) can address these concerns by integrating physics rules into deep learning methodology. This survey provides a systematic overview of PINN in power systems, summarizing different paradigms and investigating their applications and relevant research.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2023)
Article
Physics, Mathematical
Colby L. Wight, Jia Zhao
Summary: This paper focuses on using deep neural networks to design an improved Physics Informed Neural Network (PINN) for automatically solving the Allen-Cahn and Cahn-Hilliard equations. Various techniques and sampling strategies are proposed to enhance the efficiency and accuracy of the PINN in solving phase field equations, allowing for a wider applicability to a broader class of PDE problems without restriction on the explicit form of the PDEs.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mechanics
Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, Ricardo Vinuesa
Summary: This article introduces the application of Physics-informed neural networks (PINNs) in solving and identifying partial differential equations. By applying PINNs to solve boundary layer problems of the Navier-Stokes equations and simulate various turbulent flow cases, it is demonstrated that PINNs have good applicability for both laminar and turbulent flows.
Article
Computer Science, Interdisciplinary Applications
Mohammad Amin Nabian, Rini Jasmine Gladstone, Hadi Meidani
Summary: PINNs are deep neural networks trained to compute the response of systems governed by PDEs using automatic differentiation. Although successful, they still need improvements in computational efficiency, which is why this paper studies the performance of an importance sampling approach for efficient training of PINNs.
COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING
(2021)
Article
Mathematics, Applied
Zhiwei Gao, Liang Yan, Tao Zhou
Summary: In this work, an adaptive strategy called FI-PINNs is proposed for solving PDE problems. The strategy defines failure probability based on the residual and improves numerical accuracy by adding more training points. Similar to adaptive finite element methods, the approach uses failure probability as a posterior error indicator to generate new training points.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Emilio Jose Rocha Coutinho, Marcelo Dall'Aqua, Levi McClenny, Ming Zhong, Ulisses Braga-Neto, Eduardo Gildin
Summary: Physics-informed Neural Network (PINN) is a promising tool for physical phenomena described by partial differential equations (PDE), but it struggles with stiff problems that involve shocks in their solutions. Previous studies manually adjusted an artificial viscosity (AV) value to address this, but this paper proposes three methods that do not rely on predefined AV values. These methods successfully learn AV values and shock locations, and improve the approximation error.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jared O'Leary, Joel A. Paulson, Ali Mesbah
Summary: This study proposes a framework for training artificial neural networks to learn the hidden physics within stochastic differential equations (SDEs). The framework propagates stochasticity through the known structure of the SDE and utilizes automatic differentiation and mini-batch gradient descent to establish the parameters of the neural networks. The results demonstrate the potential of this method in unraveling the hidden physics of multivariate stochastic dynamical systems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Xin-Yang Liu, Jian-Xun Wang
Summary: Model-based reinforcement learning (MBRL) aims to improve sample efficiency by learning a predictive model of the environment, but the quality of the learned model is crucial for its performance. This study proposes a physics-informed MBRL framework that leverages prior knowledge of the environment's underlying physics to enhance the quality of the learned model and reduce interactions with the environment.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Water Resources
Mohammad Afzal Shadab, Dingcheng Luo, Eric Hiatt, Yiran Shen, Marc Andre Hesse
Summary: In this work, a deep learning technique called Physics Informed Neural Networks (PINNs) is used to study steady ground-water flow in unconfined aquifers. PINNs utilize both physics information represented by partial differential equations (PDEs) and data obtained from physical observations. The training of PINNs involves steady-state analytical solutions and laboratory based experiments to predict phreatic surface profiles and estimate the hydraulic conductivity. The results show that PINNs can overcome the limitations of the Dupuit-Boussinesq equation and produce better predictions by incorporating physics information from more complete flow models like the one derived by Di Nucci.
ADVANCES IN WATER RESOURCES
(2023)
Article
Mathematics, Applied
Ramzi Askri, Christophe Bois, Herve Wargnier, Julie Lecomte
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2016)
Article
Computer Science, Software Engineering
Ramzi Askri, Christophe Bois, Herve Wargnier, Nicolas Gayton
COMPUTER-AIDED DESIGN
(2018)
Article
Engineering, Multidisciplinary
Kiran Sagar Kollepara, Jose M. Navarro-Jimenez, Yves Le Guennec, Luisa Silva, Jose Aguado
Summary: This article investigates the limitations of low-rank approximations in contact mechanics and provides numerical evidence that contact pressure is linearly inseparable in many practical cases.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Engineering, Manufacturing
Ramzi Askri, Christophe Bois, Aymen Danoun
Summary: This paper introduces a method to analyze the fastening process of parts with geometric form defects, utilizing a finite element model that combines connectors and rigid surfaces to simulate the structural behavior of the joint. This approach improves calculation efficiency and accuracy by capturing the interaction between shape defects, bolt-hole clearance, and target axial preload.
CIRP JOURNAL OF MANUFACTURING SCIENCE AND TECHNOLOGY
(2021)
Proceedings Paper
Engineering, Industrial
Ramzi Askri, Christophe Bois, Herve Wargnier
14TH CIRP CAT 2016 - CIRP CONFERENCE ON COMPUTER AIDED TOLERANCING
(2016)
Proceedings Paper
Materials Science, Composites
Ramzi Askri, Christophe Bois, Herve Wargnier, Julie Lecomte
20TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
(2015)
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)