Predicting Complex Nonlinear Turbulent Systems with Uncertainty Quantification
Abstract
Complex nonlinear turbulent systems involve nonlinear interactions between different phenomena arising on each scale, strong intermi ttency and extreme events. Predicting these systems is quite challenging due to the limited observations, the enormous computational cost, and the intrinsic complexity of nature that requires a systematic uncertainty quantification (UQ). The main objective of this project is to develop new mathematical tools to facilitate the prediction of these systems. Three specific aspects are considered: 1) effective reduced order models (ROMs) for UQ, data assimilation and prediction, 2) a new Bayesian machine learning ensemble forec ast (BMLEF) algorithm for complex nonlinear systems using only partial observations, and 3) using information flow to understand the causality and predictability of complex nonlinear system.ROMs provide useful approximations of complex dynamical systems with a sig nificant reduction of the computational cost. We propose to develop a new nonlinear stochastic ROM with physics-constrained paramete rizations and solvable conditional statistics. It improves the modeling description of the large-scale dynamics while allowing effic ient and accurate data assimilation and UQ of the unresolved scale variables that advance effective forecasts. We also propose an ef ficient learning algorithm that incorporates rapid data assimilation into a Bayesian inference framework to systematically build suc h a ROM in the presence of only partial observations.Model error is one major challenge in applying the model-based ensemble forecas t. In the situation with only partial observations, machine learning (ML) cannot be directly applied for forecasts either. Here, we propose to develop a new BMLEF algorithm. It utilizes data assimilation that combines an imperfect model with partial observations t o recover the unobserved variables. The model error is mitigated in the assimilated time series, which also creates a training data set for the ML forecasts. A generalized ensemble data assimilation scheme is proposed for the initialization of the BMLEF. The BMLEF is computationally efficient in the forecast stage. It also quantifies the forecast uncertainty using an effective non-Gaussian cha racterization.Next, we propose to develop an information flow technique to understand the causality and predictability of general no nlinear systems with random noise. It will be used to understand the effect of data assimilation on the predictability and the ef t of the model error, such as in ROMs and in parameterizations, on the forecast skill. As a concrete application, the information fl ow will be applied to studying the causal relationship for different types of the events associated with the ENSO diversity, which i s a very important but hard topic in practice.The new BMLEF algorithm can be applied to many forecast problems for ocean and climate that the Navy is interested in. The proposed nonlinear stochastic ROM is applicable to many DoD-relevant contexts where complex sys tems with partial observations are involved. The information flow will facilitate the improvement of the observational networks, the data assimilation and the prediction algorithms. The new tools may assist the DoD data assimilation and forecasting systems and the US Navy Global Prediction Systems. Applying the information flow to understand the forecast of the ENSO diversity can provide usefu l information that impacts DoD strategic planning and operational capabilities in both the equatorial Pacific and the global regions . The project will also contribute to workforce development through multidisciplinary training of students.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 22, 2021
- Source ID
- N000142112904
Entities
People
- Nan Chen
Organizations
- Office of Naval Research
- United States Navy
- University of Wisconsin System