In many areas, such as the physical sciences, life sciences, and finance, control approaches are used to achieve a desired goal in complex dynamical systems governed by differential equations. In this work we formulate the problem of controlling stochastic partial differential equations (SPDE) as a reinforcement learning problem. We present a learning-based, distributed control approach for online control of a system of SPDEs with high dimensional state-action space using deep deterministic policy gradient method. We tested the performance of our method on the problem of controlling the stochastic Burgers' equation, describing a turbulent fluid flow in an infinitely large domain.
The current COVID-19 pandemic is now getting contained, albeit at the cost of more than 2.3 million human lives. A critical phase in any pandemic is the early detection of cases to develop preventive treatments and strategies. In the case of COVID-19, several studies have indicated that chest radiography images of the infected patients show characteristic abnormalities. However, at the onset of a given pandemic, such as COVID-19, there may not be sufficient data for the affected cases to train models for their robust detection. Hence, supervised classification is ill-posed for this problem because the time spent in collecting large amounts of data from infected persons could lead to the loss of human lives and delays in preventive interventions. Therefore, we formulate the problem of identifying early cases in a pandemic as an anomaly detection problem, in which the data for healthy patients is abundantly available, whereas no training data is present for the class of interest (COVID-19 in our case). To solve this problem, we present several unsupervised deep learning approaches, including convolutional and adversarially trained autoencoder. We tested two settings on a publicly available dataset (COVIDx) by training the model on chest X-rays from (i) only healthy adults, and (ii) healthy and other non-COVID-19 pneumonia, and detected COVID-19 as an anomaly. After performing 3-fold cross validation, we obtain a ROC-AUC of 0.765. These results are very encouraging and pave the way towards research for ensuring emergency preparedness in future pandemics, especially the ones that could be detected from chest X-rays.
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