Methodology for Multi Time-Scale Nonlinear Dynamical Spatio-Temporal Statistical Models

科学家和工程师越来越意识到，在试图理解复杂系统(如那些随时间和空间变化的系统)时，准确描述各种不确定性来源的重要性。这类系统的例子包括海洋加热如何影响热带对流云，进而影响北美的恶劣天气和栖息地条件；或者迁徙物种如何与其环境相互作用，以及来自捕食者和猎物的竞争压力。在对这种复杂的时空现象进行统计建模时，科学目标通常是推断、预测或预测，所有这些都需要某种程度的不确定性。为了通过建模实现这些目标，必须综合来自各种来源的信息，包括直接观测、间接(遥感)观测、替代观测(机械模型输出)、先前的经验结果、专家意见和科学知识。然后，必须将这些信息集成到一个过程模型中，该模型可以表示交互过程的复杂性，并考虑到不确定性。这项研究致力于以一种能够解释不同时间尺度上的复杂相互作用的方式来建立这些模型。该项目致力于为多时间尺度的非线性动态时空过程建立一个简洁且计算高效的模型的方法学框架，该模型以适应数据、过程和参数的不确定性的方式来考虑过程和时间尺度上的相互作用。特别是，该项目将侧重于一种混合模型，该模型将广义二次型非线性时空动态模型的元素与递归神经网络模型相结合。然而，这种方法将侧重于涉及变异性的多个时间尺度的过程的模型。这将包括开发计算效率高的算法，通过采用、扩展和结合统计学和机器学习的方法，处理与复杂相互作用的非线性现象相关的状态和参数空间中的极端维度灾难。拟议的建模和计算方法不仅将是统计学上的进步，而且将在处理复杂的多时间尺度动态过程的广泛学科中发挥作用，如脑科学、气候学、人口学、计量经济学、渔业、生态学、气象学、海洋学和野生动物生物学。此外，该项目将通过培训一名研究生研究助理来促进STEM教育，该助理将获得跨学科经验。此外，该项目将通过雇用本科生研究助理来帮助开发时空数据可视化工具，从而培养本科生对STEM学科的兴趣。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Scientists and engineers are increasingly aware of the importance of accurately characterizing various sources of uncertainty when trying to understand complex systems such as those that vary across time and space. Examples of such systems include how ocean heating influences convective clouds in the tropics, which in turn, can influence severe weather and habitat conditions over North America; or, how a migratory species interacts with its environment and competitive pressures from both predators and prey. When performing statistical modeling on such complex spatio-temporal phenomena, the scientific goal is typically either inference, prediction, or forecasting, all of which require some measure of uncertainty. To accomplish these goals through modeling, one must synthesize information from a variety of sources, including direct observations, indirect (remotely sensed) observations, surrogate observations (mechanistic model output), previous empirical results, expert opinion, and scientific knowledge. This information must then integrate into a process model that can represent the complexity of the interacting processes, and account for uncertainty. This research is concerned with building these models in a way that can account for complex interactions across different time scales.This project concerns the development of a methodological framework for parsimonious and computationally efficient models for multi time-scale nonlinear dynamical spatio-temporal processes that accounts for the interaction across processes and time scales in such a way as to accommodate uncertainty in data, processes, and parameters. In particular, the project will focus on a hybrid model that combines elements of a generalized quadratic nonlinear spatio-temporal dynamical model with a recurrent neural network model. However, this methodology will focus on models for processes that involve multiple time scales of variability. This will include the development of computationally efficient algorithms that can deal with the extreme curse of dimensionality in the state and parameter spaces associated with complex interacting nonlinear phenomena by adapting, extending and combining approaches from both statistics and machine learning. Not only will the proposed modeling and computational methodology be an advancement in statistics, but it will be useful across a broad range of disciplines that deal with complex multi time-scale dynamical processes such as brain science, climatology, demography, econometrics, fisheries, ecology, meteorology, oceanography, and wildlife biology. In addition, the project will contribute to STEM education through training a graduate research assistant, who will gain inter-disciplinary experience. In addition, the project will foster undergraduate interest in the STEM disciplines by employing undergraduate research assistants to help with the development of visualization tools for spatio-temporal data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.