Robust data assimilation with noise: Applications to cardiac dynamics
Robust data assimilation with noise: Applications to cardiac dynamics
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DOI：
10.1063/5.0033539
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发表时间：
2021-01-01
期刊：
影响因子：
2.9
通讯作者：
Cherry, Elizabeth M.
中科院分区：
文献类型：
--
作者：
Marcotte, Christopher D.;Fenton, Flavio H.;Cherry, Elizabeth M.
心脏组织中的激励模式的重建必须与由于模型误差、观测误差和隐藏状态变量而引起的不确定性相抗衡。这些状态重建的准确性可以通过努力考虑这些不确定性来源中的每一个来提高，特别是通过在模型规范和模型动态中并入不确定性。为此，我们介绍了随机建模方法的背景下，基于集合的数据同化和状态重建的心脏动力学在一维和三维心脏系统。我们提出了两类方法，一种是遵循正则随机微分方程形式主义，另一种是在模型的参数空间中扰动系综演化，根据系综中使用的模型的细节进一步表征。随机方法被施加到一个简单的模型的心脏动力学与快-慢的时间尺度分离，允许调整的形式的有效的随机同化计划的基础上类似的分离的动态时间尺度。我们发现，选择慢或快的时间尺度制定的随机强迫项可以理解类似于现有的集合膨胀技术占有限大小的影响，在集合卡尔曼滤波方法，但是，像现有的通货膨胀方法，必须小心选择相关参数，以避免过度驱动的数据同化过程。特别是，我们发现，随机过程的组合，类似于添加剂和乘法通货膨胀方法的组合，产生改进的同化误差和合奏传播这些经典的方法。
Reconstructions of excitation patterns in cardiac tissue must contend with uncertainties due to model error, observation error, and hidden state variables. The accuracy of these state reconstructions may be improved by efforts to account for each of these sources of uncertainty, in particular, through the incorporation of uncertainty in model specification and model dynamics. To this end, we introduce stochastic modeling methods in the context of ensemble-based data assimilation and state reconstruction for cardiac dynamics in one- and three-dimensional cardiac systems. We propose two classes of methods, one following the canonical stochastic differential equation formalism, and another perturbing the ensemble evolution in the parameter space of the model, which are further characterized according to the details of the models used in the ensemble. The stochastic methods are applied to a simple model of cardiac dynamics with fast-slow time-scale separation, which permits tuning the form of effective stochastic assimilation schemes based on a similar separation of dynamical time scales. We find that the selection of slow or fast time scales in the formulation of stochastic forcing terms can be understood analogously to existing ensemble inflation techniques for accounting for finite-size effects in ensemble Kalman filter methods; however, like existing inflation methods, care must be taken in choosing relevant parameters to avoid over-driving the data assimilation process. In particular, we find that a combination of stochastic processes-analogously to the combination of additive and multiplicative inflation methods-yields improvements to the assimilation error and ensemble spread over these classical methods.