`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form
Cooperative Institute for Research in Environmental Sciences（环境科学合作研究所）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Physical Sciences Laboratory（物理科学实验室）；National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局）；University of California San Diego（加利福尼亚大学圣迭戈分校）
Tse-Chun Chen, Stephen G. Penny, Timothy A. Smith, Jason A. Platt
Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the $2^\text{nd}$ order Runge-Kutta. It is shown that the NVAR emulator can be interpreted as a data-driven method used to recover the numerical integration scheme that produced the data. It is also shown that the approach can be extended to produce high-order numerical schemes directly from data. The impacts of the presence of noise and temporal sparsity in the training set is further examined to gauge the potential use of this method for more realistic applications.
On the emergence of numerical instabilities in Next Generation Reservoir Computing
Department of Electrical and Computer Engineering, Clarkson University, Potsdam, 13699, New York, U.S.A.（电气与计算机工程系，克林顿大学）；Clarkson Center for Complex Systems Science, Clarkson University, Potsdam, 13699, New York, U.S.A.（复杂系统科学中心，克林顿大学）
How more data can hurt: Instability and regularization in next-generation reservoir computing
Santa Fe Institute（圣达菲研究所）；Department of Electrical and Computer Engineering（电气与计算机工程系）；Clarkson University（克拉克逊大学）；Clarkson Center for Complex Systems Science（复杂系统科学中心）；Department of Physics（物理系）；Toronto Metropolitan University（多伦多 Metropolitan 大学）；Department of Automation（自动化系）
Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems
University of Maryland（马里兰大学）；University of Chicago（芝加哥大学）；Institute for Research in Electronics and Applied Physics (IREAP)（电子与应用物理研究所）；Institute for Physical Science and Technology (IPST)（物理科学与技术研究所）；Santa Fe Institute（圣达菲研究所）
Next-Generation Reservoir Computing for Dynamical Inference
Centre for Mathematical Science, Lund University（数学科学中心，隆德大学）；IMFUFA, Department of Science and Environment, Roskilde University（IMFUFA，科学与环境系，罗斯基尔德大学）
The Ohio State University（俄亥俄州立大学）；ResCon Technologies LLC（ResCon技术有限责任公司）；Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所（IFISC，西班牙国家研究委员会-巴利阿里群岛大学））；The University of Tokyo（东京大学）
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学研究所）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University Berlin（柏林洪堡大学物理系）；Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究所）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学教育部量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
Complexity-calibrated Benchmarks for Machine Learning Reveal When Next-Generation Reservoir Computer Predictions Succeed and Mislead
W. M. Keck Science Department of Pitzer, Scripps, and Claremont McKenna College（皮泽学院、斯克里普斯学院和克莱蒙特·麦肯纳学院W.M.凯克科学系）；Nanyang Technological University（南洋理工大学）；University of California at Davis（加州大学戴维斯分校）
Exploring the limits of multifunctionality across different reservoir computers
University College Cork（科克大学学院）；Ludwig-Maximilians University Munich（慕尼黑路德维希-马克西米利安大学）；Collins Aerospace（柯林斯航空航天公司）；Deutsches Zentrum für Luft-und Raumfahrt（德国航空航天中心）
Predicting Chaotic System Behavior using Machine Learning Techniques
School of Electrical and Computer Engineering, Georgia Institute of Technology（电气与计算机工程学院，佐治亚理工学院）；School of Electrical and Automation Engineering, East China Jiaotong University（电气自动化工程学院，东华交通大学）
