We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter, and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.
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）
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）
