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Stochastic nonlinear dynamical systems are ubiquitous in modern, real-worldapplications. Yet, estimating the unknown parameters of stochastic, nonlineardynamical models remains a challenging problem. The majority of existingmethods employ maximum likelihood or Bayesian estimation. However, thesemethods suffer from some limitations, most notably the substantialcomputational time for inference coupled with limited flexibility inapplication. In this work, we propose DeepBayes estimators that leverage thepower of deep recurrent neural networks in learning an estimator. The methodconsists of first training a recurrent neural network to minimize themean-squared estimation error over a set of synthetically generated data usingmodels drawn from the model set of interest. The a priori trained estimator canthen be used directly for inference by evaluating the network with theestimation data. The deep recurrent neural network architectures can be trainedoffline and ensure significant time savings during inference. We experimentwith two popular recurrent neural networks -- long short term memory network(LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of ourproposed method on different example models and perform detailed comparisonswith state-of-the-art approaches. We also provide a study on a real-worldnonlinear benchmark problem. The experimental evaluations show that theproposed approach is asymptotically as good as the Bayes estimator.

DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models