Data assimilation (DA) is integrated with machine learning in order to perform entirely data‐driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as pretrained surrogate models to replace key components of the DA cycle in numerical weather prediction (NWP), including the conventional numerical forecast model, the forecast error covariance matrix, and the tangent linear and adjoint models. It is shown how these RNNs can be initialized using DA methods to directly update the hidden/reservoir state with observations of the target system. The results indicate that these techniques can be applied to estimate the state of a system for the repeated initialization of short‐term forecasts, even in the absence of a traditional numerical forecast model. Further, it is demonstrated how these integrated RNN‐DA methods can scale to higher dimensions by applying domain localization and parallelization, providing a path for practical applications in NWP.

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Constitutive relationships (i.e., flow laws) relate strain rate () to differential stress (σ), temperature (T), pressure (P), water fugacity ( H O 2 f ), and material properties for a given deformation mechanism. As one of the most abundant minerals in the crust, quartz is thought to control crustal rheology and is commonly used to model and predict the viscous behavior of the middle and lower crust (e.g., Brace & Kohlstedt, 1980;Hirth et al., 2001). At these depths, quartz deforms by dislocation creep, a thermally activated process that is driven by the nucleation, buildup, and motion of dislocations, resulting in viscous flow. Dislocation creep

For the Research Topic Data Assimilation and Control: Theory and Applications in Life Sciences we first review the formulation of statistical data assimilation (SDA) and discuss algorithms for exploring variational approximations to the conditional expected values of biophysical aspects of functional neural circuits. Then we report on the application of SDA to (1) the exploration of properties of individual neurons in the HVC nucleus of the avian song system, and (2) characterizing individual neurons formulated as very large scale integration (VLSI) analog circuits with a goal of building functional, biophysically realistic, VLSI representations of functional nervous systems. Networks of neurons pose a substantially greater challenge, and we comment on formulating experiments to probe the properties, especially the functional connectivity, in song command circuits within HVC.