Machine learning can be enhanced through the integration of external knowledge. This method, called knowledge informed machine learning, is also applicable within the field of Prognostics and Health Management (PHM). In this paper, the various methods of knowledge informed machine learning, from a PHM context, are reviewed with the goal of helping the reader understand the domain. In addition, a knowledge informed machine learning technique is demonstrated, using the common IMS and PRONOSTIA bearing data sets, for remaining useful life (RUL) prediction. Specifically, knowledge is garnered from the field of reliability engineering which is represented through the Weibull distribution. The knowledge is then integrated into a neural network through a novel Weibull-based loss function. A thorough statistical analysis of the Weibull-based loss function is conducted, demonstrating the effectiveness of the method on the PRONOSTIA data set. However, the Weibull-based loss function is less effective on the IMS data set. The results, shortcomings, and benefits of the approach are discussed in length. Finally, all the code is publicly available for the benefit of other researchers.
Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators
Tsinghua University（清华大学）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（雁栖湖北京数学科学与应用研究院）
A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks
Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Center for Mathematical Machine Learning and its Applications (CM2LA), Department of Mathematics, Pohang University of Science and Technology（浦项科技大学数学系数学机器学习及其应用中心(CM2LA)）；Department of Mathematics, Gyeongsang National University（庆尚国立大学数学系）；Research Institute of Mathematics, Seoul National University（首尔大学数学研究所）
On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks
Know-Center GmbH – Research Center for Data-Driven Business & Big Data Analytics（知识中心有限公司——数据驱动业务与大数据分析研究中心）；LEC GmbH – Large Engines Competence Center（大型发动机竞争力中心有限公司）
Physics-informed DeepONet with stiffness-based loss functions for structural response prediction
New York University Abu Dhabi（纽约大学阿布扎比分校）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Mansoura University（曼苏拉大学）
Gryphon Center for Artificial Intelligence and Theoretical Sciences（格里芬人工智能与理论科学中心）；Georgia Institute of Technology（佐治亚理工学院）；University of Pennsylvania（宾夕法尼亚大学）
Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving
College of Engineering and Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；Center for AI Research, VinUniversity（VinUniversity人工智能研究中心）；Group of Materials and Structures, School of Mechanical Engineering, Hanoi University of Science and Technology（河内科技大学机械工程学院材料与结构组）；Department of Mathematics and Informatics, Hanoi University of Science and Technology（河内科技大学数学与信息学系）
Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching
School of Mathematics and Statistics（数学与统计学学院）；Huazhong University of Science and Technology（华中科技大学）；Northwestern Polytechnical University（西北工业大学）
Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
The University of Tokyo, Japan（东京大学）；Axiom Research Group（Axiom研究组）；Department of Applied Mathematics and Computational Science, NM-AIST, Tanzania（应用数学与计算科学系，NM-AIST，坦桑尼亚）；African Institute for Mathematical Sciences (AIMS), Research and Innovation Centre, Rwanda（非洲数学科学研究所（AIMS），研究与创新中心，卢旺达）
Training Variation of Physically-Informed Deep Learning Models
Department of Materials Science and Engineering（材料科学与工程系）；The Ohio State University（俄亥俄州立大学）；Center for Integrated Nanotechnologies（集成纳米技术中心）；Sandia National Laboratories（桑迪亚国家实验室）；BlueQuartz Software（BlueQuartz软件公司）；Department of Mechanical and Aerospace Engineering（机械与航空航天工程系）
Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Network
School of Computer Science and Technology, Anhui University（安徽大学计算机科学与技术学院）；Tongling University（铜陵大学）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）
A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning
Université Jean Monnet Saint-Étienne, CNRS, Institut d’Optique Graduate School, Laboratoire Hubert Curien UMR 5516（里昂蒙特大学圣埃蒂安分校、法国国家科学研究中心、光学研究生院、Hubert Curien实验室 UMR 5516）；Inria and University College London, France and United Kingdom（Inria 和 英国伦敦大学学院，法国和英国）
Dual-Balancing for Physics-Informed Neural Networks
Department of Computer Science, Hong Kong Baptist University（香港 Baptist 大学计算机科学系）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（高性能计算研究所（IHPC），科技研究局（A*STAR））
