Bayesian spatiotemporal modeling for inverse problems
Bayesian spatiotemporal modeling for inverse problems
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DOI：
10.1007/s11222-023-10253-z
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发表时间：
2022-04
影响因子：
2.2
通讯作者：
Shiwei Lan;Shuyi Li;M. Pasha
中科院分区：
文献类型：
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作者：
Shiwei Lan;Shuyi Li;M. Pasha
时空观测的反问题在科学研究和工程应用中普遍存在。在这些时空反问题中，观察到的多元时间序列用于推断物理或生物兴趣的参数。这些问题的传统解决方案通常忽略数据中的空间或时间相关性（静态模型），或者简单地对随时间推移汇总的数据进行建模（时间平均模型）。无论哪种情况，包含时空相互作用的数据信息都没有充分用于参数学习，这导致这些问题的建模不充分。在本文中，我们应用基于时空高斯过程（STGP）的贝叶斯模型来反演时空数据问题，并表明时空信息提供了更有效的参数估计和不确定性量化（UQ）。我们使用依赖时间的平流扩散偏微分方程（PDE）和三个混沌常微分方程（ODE）证明了贝叶斯时空建模反问题的优点，与传统的静态和时间平均方法相比。我们还为时空建模拟合轨迹的优越性提供了理论依据，即使它看起来很麻烦（例如对于混沌动力学）。
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or biological interests. Traditional solutions for these problems often ignore the spatial or temporal correlations in the data (static model), or simply model the data summarized over time (time-averaged model). In either case, the data information that contains the spatiotemporal interactions is not fully utilized for parameter learning, which leads to insufficient modeling in these problems. In this paper, we apply Bayesian models based on spatiotemporal Gaussian processess (STGP) to inverse problems with spatiotemporal data and show that the spatial and temporal information provides more effective parameter estimation and uncertainty quantification (UQ). We demonstrate the merit of Bayesian spatiotemporal modeling for inverse problems compared with traditional static and time-averaged approaches using a time-dependent advection–diffusion partial different equation (PDE) and three chaotic ordinary differential equations (ODE). We also provide theoretic justification for the superiority of spatiotemporal modeling to fit the trajectories even if it appears cumbersome (e.g. for chaotic dynamics).