Скачать или смотреть Causality-Based Learning || Extreme Event Aware (η-) Learning || Oct 24, 2025

Speakers, institutes & titles
1) Yinling Zhang, University of Wisconsin Madison, Combining Stochastic Model with Machine A Causality-Based Learning Approach for System Identification and Data
Assimilation of Complex Dynamical Systems and Applications
Abstract: Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, an iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to the stochastic noise. A practical algorithm is designed to facilitate the causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables with conditional Gaussian structure. This structure enables closed analytic formulas for efficient nonlinear data assimilation, which are exploited to sample the trajectories of the unobserved variables with rigorous uncertainty quantification. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure, which mitigate the curse of dimensionality and prevent the finite time blow-up issue. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events. This unified approach to quantify uncertainty and prediction has broad applicability to complex systems with sparse observations across climate science, materials engineering, and beyond.

2) Kai Chang, Massachusetts Institute of Technology (MIT), Extreme Event Aware (η-) Learning
Abstract: Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems. Many practical challenges arise from the infrequency and severity of these events, including the considerable variance of simple sampling methods and the substantial computational cost of high-fidelity numerical simulations. Numerous data-driven methods have recently been developed to tackle these challenges. However, a typical assumption for the success of these methods is the occurrence of multiple extreme events, either within the training dataset or during the sampling process. This leads to accurate models in regions of quiescent events but with high epistemic uncertainty in regions associated with extremes. To overcome this limitation, we introduce Extreme Event Aware (e2a or eta) or η-learning which does not assume the existence of extreme events in the available data. η-learning reduces the uncertainty even in “uncharted” extreme event regions, by enforcing the extreme event statistics of an observable indicative of extremeness during training, which can be available through qualitative arguments or estimated with unlabeled data. This type of statistical regularization results in models that fit the observed data, while enforcing consistency with the prescribed observable statistics, enabling the generation of unprecedented extreme events even when the training data lack extremes therein. Theoretical results based on optimal transport offer a rigorous justification and highlight the optimality of the introduced method. Additionally, extensive numerical experiments illustrate the favorable properties of the η-learning framework on several prototype problems and real-world precipitation downscaling problems.