Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires experimental measurements of the system input and output, but it can be difficult to determine whether inaccuracies in the model stem from modelling errors or noise. This paper presents a novel method to identify the causal component of the input-output data from measurements of a system in the presence of output noise, as a function of frequency, without needing a high fidelity model. An output prediction, calculated using an available model, is optimally combined with noisy measurements of the output to predict the input to the system. The parameters of the algorithm balance the two output signals and are utilised to calculate a nonlinear coherence metric as a measure of causality. This method is applicable to a broad class of nonlinear dynamical systems. There are currently no solutions to this problem in the absence of a complete benchmark model.
Modeling Time-evolving Causality over Data Streams
SANKEN, Osaka University（SANKEN，大阪大学）；Institute for Clarity in Documentation（文档清晰研究所）；Inria Paris-Rocquencourt（巴黎-鲁克勒特研究所）；Rajiv Gandhi University（拉贾·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕勒姆研究实验室）
Northwestern Polytechnical University（西北工业大学）；Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences（中国科学院分子细胞科学卓越创新中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；South China University of Technology（华南理工大学）；Guangdong Institute of Intelligence Science and Technology（广东智能科学技术研究院）；Fudan University（复旦大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）
Deciphering interventional dynamical causality from non-intervention complex systems
Research Institute of Intelligent Complex Systems & CISOR, Fudan University（智能复杂系统研究所及CISOR，复旦大学）；International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo（神经智能国际研究中心，东京大学先进研究所，东京大学）；School of Pharmacy, Shanghai University of Traditional Chinese Medicine（上海中医药大学药学院）；Institute of AI and Robotics, College of Intelligent Robotics and Advanced Manufacturing, Fudan University（人工智能与机器人研究所，智能机器人与先进制造学院，复旦大学）；Frontiers Science Center for Deep Ocean Multispheres and Earth System, Key Laboratory of Marine Chemistry Theory and Technology, Ministry of Education, Ocean University of China（深海多球体与地球系统前沿科学中心，海洋化学理论与技术重点实验室，教育部，中国海洋大学）；School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University（数学科学学院和人工智能学院，上海交通大学）；Key Laboratory of Systems Health Science of Zhejiang Province, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences（浙江省系统健康科学重点实验室，杭州高级研究所，中国科学院大学，中国科学院）
Learning by Doing: Controlling a Dynamical System using Causality, Control, and Reinforcement Learning
University of Copenhagen（哥本哈根大学）；Lund University（隆德大学）；Carnegie Mellon University（卡内基梅隆大学）；Uppsala University（乌普萨拉大学）；Université Paris-Saclay（巴黎萨克雷大学）；RWTH Aachen University（亚琛工业大学）
A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
