Article
Engineering, Aerospace
Yunyang Feng, Xizhen Song, Wei Yuan, Hanan Lu
Summary: This paper discusses the importance of empirical models in the design of aero-engine compressors, and identifies the limitations of existing empirical models. To address these issues, a physics-informed deep learning model is proposed, which significantly improves the design performance and flow field prediction accuracy of the compressor.
AEROSPACE SCIENCE AND TECHNOLOGY
(2023)
Article
Engineering, Industrial
Yilin Li, Jinjiang Wang, Zuguang Huang, Robert X. Gao
Summary: This paper introduces a new physics-informed meta-learning framework for tool wear prediction under varying wear rates, improving prediction accuracy by enhancing modeling strategy and constraining optimization process with a loss term informed by physics.
JOURNAL OF MANUFACTURING SYSTEMS
(2022)
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
Computer Science, Artificial Intelligence
Zixue Xiang, Wei Peng, Xu Liu, Wen Yao
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, Multidisciplinary
Mingyuan Yang, John T. Foster
Summary: In this paper, a multi-output physics-informed neural network (MO-PINN) is proposed to provide solutions with uncertainty distributions for both forward and inverse PDE problems with noisy data. It is demonstrated that MO-PINN can provide accurate predictions and its solutions are consistent with traditional methods. Additional statistical knowledge can be incorporated to improve the prediction if available.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Levi D. McClenny, Ulisses M. Braga-Neto
Summary: Physics-Informed Neural Networks (PINNs) are a promising application of deep neural networks for the numerical solution of nonlinear partial differential equations (PDEs). In this paper, a fundamentally new way to train PINNs adaptively is proposed, where fully trainable adaptation weights are applied to each training point individually, enabling the neural network to autonomously learn the difficult regions of the solution and focus on them. The self-adaptation weights provide a soft multiplicative soft attention mask resembling mechanisms used in computer vision. In numerical experiments, the proposed SA-PINN outperforms other state-of-the-art PINN algorithms in L2 error with fewer training epochs.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Applied
Linlin Zhong, Bingyu Wu, Yifan Wang
Summary: This work proposes a meta-learning method called Meta-PINN to reduce the training time of PINN-based 1D arc simulation. By training the meta network on various plasma modeling tasks, it can initialize the PINN-based network for new tasks. The results from four different 1D arc models demonstrate that Meta-PINN is an effective method for accelerating the PINN-based simulation, achieving a speed-up ranging from 1.1x to 6.9x in terms of relative L-2 error. Rating: 8/10.
JOURNAL OF PHYSICS D-APPLIED PHYSICS
(2023)
Article
Chemistry, Analytical
Sai Karthikeya Vemuri, Joachim Denzler
Summary: Modeling and simulating complex non-linear systems is important in various fields. Neural networks are commonly used for such tasks but require large amounts of data. Physics-Informed Neural Networks (PINNs) combine physics knowledge with neural networks, providing a powerful tool for solving differential equation problems. This paper proposes gradient statistics-based weighting schemes for PINNs to improve their performance and compares them on 2D Poisson's and Klein-Gordon's equations.
Article
Engineering, Multidisciplinary
Jianchuan Yang, Xuanqi Liu, Yu Diao, Xi Chen, Haikuo Hu
Summary: In this paper, the advantages and limitations of physics-informed neural networks (PINNs) are discussed, and a strategy of task decomposition and progressive learning is proposed to overcome the limitations and improve performance. Through task decomposition and decomposition of loss terms, they successfully overcome the limitations of existing methods and demonstrate better performance in experiments.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Review
Chemistry, Multidisciplinary
Joseph Pateras, Pratip Rana, Preetam Ghosh
Summary: Physics-informed machine learning (PIML) is an emerging field that utilizes physically relevant prior information to extract physically relevant solutions from data lacking in quantity and veracity. This paper discusses recent advancements in PIML and highlights novel methods and applications of domain decomposition in physics-informed neural networks (PINNs). It also explores the use of neural operator learning to intuit relationships in physics systems traditionally modeled with complex governing equations and expensive differentiation techniques. Additionally, the paper discusses the limitations and applications of traditional physics-informed machine learning, and proposes a novel taxonomic structure to categorize PIML based on the derivation and injection of physics information into the machine learning process.
APPLIED SCIENCES-BASEL
(2023)
Article
Engineering, Multidisciplinary
David Dalton, Dirk Husmeier, Hao Gao
Summary: Modern computational soft-tissue mechanics models have the potential to provide unique patient-specific diagnostic insights, but their deployment in clinical settings has been limited by the high computational costs of conventional numerical solvers. In this study, we propose an emulation framework for soft-tissue mechanics using a Graph Neural Network (GNN) and physics-informed training, which allows for highly accurate and efficient predictions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Khang A. Luong, Thang Le-Duc, Jaehong Lee
Summary: Exact boundary conditions imposition becomes challenging when dealing with complex geometric domains or important BCs selection. To overcome this limitation, an unified physics-informed neural network (UPINN) model is introduced, with trial functions provided by deep neural networks (DNNs). The UPINN combines two phases: the first phase finds DNN-based trial functions satisfying essential BCs, and the second phase solves BVPs using exact BCs imposition procedure to constrain network outputs. The UPINN demonstrates improved prediction accuracy and training cost for solid mechanics problems with various BCs, even in the presence of complex restrictions.
ENGINEERING WITH COMPUTERS
(2023)
Article
Engineering, Multidisciplinary
N. Navaneeth, Tapas Tripura, Souvik Chakraborty
Summary: Deep neural operators are effective for learning solution operators of complex PDEs. The Wavelet Neural Operator is able to capture spatial manifolds effectively. However, relying on conventional solvers for data generation is challenging in practical applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Shivam Sharma, Rajneesh Awasthi, Yedlabala Sudhir Sastry, Pattabhi Ramaiah Budarapu
Summary: With the growth of computational resources and data generation, deep machine learning has been successfully applied in various applications. Physics-informed neural networks are developed to solve differential equations by embedding initial and boundary conditions in the cost function of artificial neural networks using algorithmic differentiation.
JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE A
(2021)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)