As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain multiple physical quantities and complex initial boundary conditions, thus PINNs often returns incorrect results. Here we take heat transfer problem in multilayer fabrics as a typical example. It is coupled by multiple temperature fields with strong correlation, and the values of variables are extremely unbalanced among different dimensions. We clarify the potential difficulties of solving such problems by classic PINNs, and propose a parallel physics-informed neural networks with bidirectional balance. In detail, our parallel solving framework synchronously fits coupled equations through several multilayer perceptions. Moreover, we design two modules to balance forward process of data and back-propagation process of loss gradient. This bidirectional balance not only enables the whole network to converge stably, but also helps to fully learn various physical conditions in PDEs. We provide a series of ablation experiments to verify the effectiveness of the proposed methods. The results show that our approach makes the PINNs unsolvable problem solvable, and achieves excellent solving accuracy.
Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations
Department of Applied Mathematics and Computer Science (DTU Compute)（应用数学与计算机科学系（DTU Compute））；Technical University of Denmark（丹麦技术大学）
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine l…
Simulation of a closed-loop dc-dc converter using a physics-informed neural network-based model
Department of Mathematics, Informatics, and Engineering, Université du Québec à Rimouski（数学、信息学与工程系，魁北克大学拉莫纳学院）；Department of Electrical Engineering, Polytechnique Montréal（电气工程系，蒙特利尔理工学院）
This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during training, the proposed framework uses a simple strategy with no added computational complexity for selecting scalar weights that balance the interplay between different terms in the physics-based loss function. In addition, we highlight a fundamental challenge involving the selection of appropriate model outputs so that the mechanical problem can be faithfull…
Physics-Informed Neural Network Digital Twin for Dynamic Tray-Wise Modeling of Distillation Columns under Transient Operating Conditions
Department of Chemical Engineering, Veer Surendra Sai University of Technology（维杰·苏雷纳·赛大学化学工程系）；Department of Computer Science & Engineering, Veer Surendra Sai University of Technology（维杰·苏雷纳·赛大学计算机科学与工程系）
A Physics Informed Neural Network (PINN) Methodology for Coupled Moving Boundary PDEs
Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay（印度理工学院孟买分校机器智能与数据科学中心）；Department of Mechanical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校机械工程系）
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in scenarios of reconstructing the physics field and solving the inverse problem. Considering the advantages of parameter sharing, spatial feature extraction and low inference cost, convolutional neural networks (CNN) are increasingly used in PINN. However, some challenges still remain as follows. To adapt convolutional PINN to solve different PDEs, considerable effo…
By integrating domain knowledge with labeled samples, informed machine learning has been emerging to improve the learning performance for a wide range of applications. Nonetheless, rigorous understanding of the role of injected domain knowledge has been under-explored. In this paper, we consider an informed deep neural network (DNN) with over-parameterization and domain knowledge integrated into its training objective function, and study how and why domain knowledge benefits the performance. Concretely, we quantitatively demonstrate the two benefits of domain knowledge in informed learning - r…
Modulated differentiable STFT and balanced spectrum metric for freight train wheelset bearing cross-machine transfer monitoring under speed fluctuations
State Key Laboratory of Advanced Rail Autonomous Operation（先进轨道交通自主运行状态重点实验室）；Beijing Jiaotong University（北京交通大学）；School of Mechanical, Electronic and Control Engineering（机械电子控制工程学院）
Multi-Joint Physics-Informed Deep Learning Framework for Time-Efficient Inverse Dynamics
School of Electronic and Electrical Engineering, University of Leeds（利兹大学电子与电气工程学院）；Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, School of Mechanical Engineering, Tianjin University（教育部机制理论与装备设计重点实验室，天津大学机械工程学院）；College of Intelligent Systems Science and Engineering, Hubei Minzu University（湖北民族大学智能系统科学与工程学院）
Institute of Information Science, Beijing Jiaotong University（北京交通大学信息科学研究所）；Beijing Key Laboratory of Advanced Information Science and Network Technology（北京市先进信息科学与网络技术重点实验室）；NLPR, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所模式识别国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Graph representation learning aims to encode all nodes of a graph into low-dimensional vectors that will serve as input of many compute vision tasks. However, most existing algorithms ignore the existence of inherent data distribution and even noises. This may significantly increase the phenomenon of over-fitting and deteriorate the testing accuracy. In this paper, we propose a Distribution-induced Bidirectional Generative Adversarial Network (named DBGAN) for graph representation learning. Instead of the widely used normal distribution assumption, the prior distribution of latent representati…
Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations
School of Science, Harbin Institute of Technology, Shenzhen, China（哈尔滨工业大学深圳校区科学学院）；Department of Theoretical Physics（理论物理系）；Applied Mathematics, University of Cambridge, Cambridge, United Kingdom（应用数学系，剑桥大学，英国）
University of Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Climate change increases the number of extreme weather events (wind and snowstorms, heavy rains, wildfires) that compromise power system reliability and lead to multiple equipment failures. Real-time and accurate detecting of potential line failures is the first step to mitigating the extreme weather impact and activating emergency controls. Power balance equations nonlinearity, increased uncertainty in generation during extreme events, and lack of grid observability compromise the efficiency of traditional data-driven failure detection methods. At the same time, modern problem-oblivious machi…
Physically-informed change-point kernels for structural dynamics
Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom（谢菲尔德大学机械工程系动力学研究组）
PIER: Physics-Informed Environmental Retrieval for Time-Series Modeling
University of Pittsburgh（匹兹堡大学）；University of Alabama（阿拉巴马大学）；University of Minnesota（明尼苏达大学）；Aarhus University（奥胡斯大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；University of Maryland（马里兰大学）
