Stochastic Modeling and Data Assimilation for Complex Dynamical Systems (W911NF-17-S-0002-12)
Abstract
Complex nonlinear turbulent systems involve nonlinear interactions between different phenomena arising on each scale, strong intermittency and extreme events. One of the main difficulties in studying these complex systems comes from the intrinsic uncertainty, which is due to the lack of a perfect understanding of nature, the practical limitation of computational resolution, and the availability of only partial observational data. Therefore, great challenges exist for modeling and understanding these systems; and it is these challenges at which the proposal is aimed. Three aspects in mathematical modeling and data assimilation are proposed in this project. First, a causality-based data-driven stochastic modeling framework is proposed, which incorporates certain pre-determined physics knowledge via information theory and the partial observations to simultaneously learn the nonlinear dynamics of the observed variables and build suitable stochastic parameterization of the unobserved components. The causation entropy developed here also allows a systematic way to correct the model error and impose a non-parametric closure to the physical models. In addition to establishing the general mathematical framework, the new method will be applied to discover the large-scale dynamics of the El Nino complexity, which is an extremely important topic in climate science and has large societal impacts. Second, a hybrid multiscale non-Gaussian data assimilation framework is proposed for many turbulent systems in fluids, geophysics and engineering problems. The goal is to build suitable stochastic forecast models with a minimum approximation such that particle methods are only needed in a low-dimensional subspace while the remaining high-dimensional subspace can be handled via closed analytic formula for efficient data assimilation of many nonlinear and non-Gaussian phenomena. Furthermore, certain constraints, including the general physics constraints and bounds of state variables, will be incorporated into the multiscale data assimilation framework. Third, a new state estimation approach that combines suitable reduced order stochastic models with machine learning is proposed to facilitate the state estimation of highly complicated nonlinear systems from only partial observations. Appropriate uncertainty quantification of the estimated states is also highlighted in this new method. The proposed nonlinear stochastic models and data assimilation methods are applicable to many Army- and DoD-relevant contexts where complex systems and incomplete observations are involved. The causality-based data-driven modeling framework can facilitate the development of stochastic parameterizations, correct the model error and combine with non-parametric methods to build closures. These broad applications, together with the proposed study of the ENSO complexity and many other nature science and engineering problems can provide potentially useful information that impacts Army strategic planning and operational capabilities in both the local and global regions. The multiscale data assimilation allows an efficient way to quantify the uncertainty in the recovered states and the resulting non-Gaussian distribution plays a crucial role in accessing the possibility of the occurrence of the extreme events, which are important topics related to the Army Mission. Finally, combining suitable reduced order models with machine learning tools for the state estimation of complicated models, including in particular the operational models, may assist the Army and the DoD data assimilation and forecasting systems. The project will also contribute to workforce development through multidisciplinary training of students.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 19, 2023
- Source ID
- W911NF2310118
Entities
People
- Nan Chen
Organizations
- Army Contracting Command
- United States Army
- University of Wisconsin–Madison