Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting nonlinear dynamical systems. However, modeling and forecasting the dynamics of chaotic systems remains an open research problem since training deep learning models requires big data, which is not always available in many cases. Such deep learners can be trained from additional information obtained from simulated results and by enforcing the physical laws of the chaotic systems. This paper considers extreme events and their dynamics and proposes elegant models based on deep neural networks, called knowledge-based deep learning (KDL). Our proposed KDL can learn the complex patterns governing chaotic systems by jointly training on real and simulated data directly from the dynamics and their differential equations. This knowledge is transferred to model and forecast real-world chaotic events exhibiting extreme behavior. We validate the efficiency of our model by assessing it on three real-world benchmark datasets: El Nino sea surface temperature, San Juan Dengue viral infection, and Bjørnøya daily precipitation, all governed by extreme events' dynamics. Using prior knowledge of extreme events and physics-based loss functions to lead the neural network learning, we ensure physically consistent, generalizable, and accurate forecasting, even in a small data regime.
Improved deep learning of chaotic dynamical systems with multistep penalty losses
School of Information Sciences and Technology（信息科学与技术学院）；Pennsylvania State University（宾夕法尼亚州立大学）；Center for Applied Scientific Computing（应用科学计算中心）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of California Santa Cruz（加州大学圣克鲁兹分校）
Coarse Graining with Neural Operators for Simulating Chaotic Systems
Department of Computing and Mathematical Sciences, California Institute of Technology（计算与数学科学系，加利福尼亚理工学院）；NVIDIA Research（NVIDIA研究）；Graduate Aerospace Laboratories, California Institute of Technology（航空航天实验室，加利福尼亚理工学院）
Turning Time Series into Algebraic Equations: Symbolic Machine Learning for Interpretable Modeling of Chaotic Time Series
SAFIR, Sorbonne University Abu Dhabi, UAE（SAFIR，索邦大学阿布扎赫德分校）；Sorbonne Center for Artificial Intelligence, Sorbonne University, Paris, France（索邦人工智能中心，索邦大学巴黎分校）
The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling
Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany（海德堡大学交叉科学计算中心）；Faculty of Mathematics and Computer Science, Heidelberg University, Germany（海德堡大学数学与计算机科学学院）；Dept. of Theoretical Neuroscience, Central Institute of Mental Health (CIMH), Mannheim, Germany（曼海姆中央心理健康研究所理论神经科学部门）；Faculty of Physics and Astronomy, Heidelberg University, Germany（海德堡大学物理与天文学学院）；Hector Institute for AI in Psychiatry and Dept. of Psychiatry and Psychotherapy, CIMH, Mannheim, Germany（曼海姆中央心理健康研究所精神病AI研究所及精神病学与心理学系）；Hertie Institute for AI in Brain Health, University of Tübingen, Germany（图宾根大学脑健康AI研究所）
Data-driven ODE modeling of the high-frequency complex dynamics via a low-frequency dynamics model
Faculty of Commerce and Management, Hitotsubashi University（一桥大学经营学部）；The Graduate School of Environment, Life, Natural Science and Technology, Okayama University（冈山大学环境生命自然科学技术研究院）；Graduate School of Business Administration, Hitotsubashi University（一桥大学经营管理研究科）
Deficiency of equation-finding approach to data-driven modeling of dynamical systems
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA（电气、计算机与能源工程学院，亚利桑那州立大学）；School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK（计算与数学科学学院，莱斯特大学）；Department of Physics, Arizona State University, Tempe, Arizona 85287, USA（物理系，亚利桑那州立大学）
A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
School of Construction, University North Carolina at Charlotte（北卡罗来纳大学夏洛特分校建筑学院）；College of Information Sciences and Technology, The Pennsylvania State University（宾夕法尼亚州立大学信息科学与技术学院）；Department of Mathematics, Institute for Computational and Data Sciences, The Pennsylvania State University（宾夕法尼亚州立大学数学系与计算和数据科学研究所）；School of Mechanical Engineering, Purdue University（普渡大学机械工程学院）
