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.

翻译：[翻译摘要] 用于多种需求的海洋生态系统预测动力学模型，因观测数据稀疏且对海洋过程复杂性的理解有限而存在显著不确定性。模型不确定性体现在参数值、多样化参数化方案的功能形式、所需复杂性水平以及状态场中。我们提出一种贝叶斯模型学习方法，能够在候选模型空间中进行插值，并从含噪、稀疏及间接观测中发现新模型，同时估计状态场与参数值以及所有学习量的联合概率密度函数。通过状态增广与计算高效的高斯混合模型-多目标差分进化滤波器，我们解决了由偏微分方程控制的高维与多学科动力学挑战。创新点包括：采用随机公式化与复杂性参数将候选模型统一为单一通用模型，以及在分段函数逼近中引入随机展开参数以生成密集候选模型空间。这些创新能够处理大量兼容且嵌套的候选模型（其中可能无一精确），并学习难以捉摸的未知功能形式。我们的新方法具有可推广性、可解释性，且能够外推至模型空间之外发现新模型。我们基于绕流山脊的三至五组分生态系统模型（包含混沌平流过程）开展系列孪生实验。通过贝叶斯定律联合更新已知、不确定及未知模型构型以及状态场与参数的先验概率。非高斯统计特性、模糊性及偏差均被捕获。识别出最能解释数据的参数值与模型构型。当观测信息充分时，模型复杂度与功能形式得以发现。