论文标题
贝叶斯对耦合生物地球化学模型的学习
Bayesian Learning of Coupled Biogeochemical-Physical Models
论文作者
论文摘要
海洋生态系统的预测动力学模型用于多种需求。由于稀疏的测量和对无数海洋过程的了解有限,因此存在明显的不确定性。参数值,具有不同参数化的功能形式,所需的复杂性水平以及在状态字段中存在模型不确定性。我们开发了一种贝叶斯模型学习方法,该方法允许在候选模型的空间中进行插值,并从嘈杂,稀疏和间接观察结果中发现新模型,同时估计了所有学到的数量的状态字段和参数值以及所有学识关的关节PDF。我们通过使用状态增强和计算有效的GMM-DO滤波器来解决由PDES控制的高维和多学科动力学的挑战。我们的创新包括随机配方和复杂性参数,以将候选模型统一为单个通用模型以及分段功能近似中的随机扩展参数,以生成密集的候选模型空间。这些创新允许处理许多兼容和嵌入式候选模型,这些模型可能没有准确,并且学习难以捉摸的未知功能形式。我们的新方法是可推广的,可解释的,并且可以从模型的空间中推断出来,以发现新的方法。我们根据山脊经过的流量以及三到五个组件的生态系统模型,进行一系列双重实验,包括具有混乱的对流的流。使用贝叶斯定律共同更新了已知,不确定和未知模型公式以及状态领域和参数的概率。非高斯统计,歧义和偏见被捕获。可以确定最能解释数据的参数值和模型公式。当观察结果足够丰富时,会发现模型的复杂性和功能。
Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, level of complexity needed, and thus in the state fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state fields and parameter values, as well as the joint PDFs of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by PDEs by using state augmentation and the computationally efficient GMM-DO filter. Our innovations include stochastic formulation and complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms. Our new methodology is generalizable, interpretable, and extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. The probabilities of known, uncertain, and unknown model formulations, and of state fields and parameters, are updated jointly using Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and model formulations that best explain the data are identified. When observations are sufficiently informative, model complexity and functions are discovered.