Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices

Petrov–Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best approximation in terms of a problem-dependent energy norm. This ideal approach has two shortcomings: first, we need to explicitly know the set of optimal test functions; and second, the optimal test functions may have large supports inducing expensive dense linear systems. A concise proposal on how to overcome these shortcomings has been raised during the last decade by the Discontinuous Petrov–Galerkin (DPG) methodology. However, DPG has also some limitations and difficulties: the method requires ultraweak variational formulations, obtained through a hybridization process, which is not trivial to implement at the discrete level. Our motivation is to offer a simpler alternative for the case of parametric PDEs, which can be used with any variational formulation. Indeed, parametric families of PDEs are an example where it is worth investing some (offline) computational effort to obtain stabilized linear systems that can be solved efficiently in an online stage, for a given range of parameters. Therefore, as a remedy for the first shortcoming, we explicitly compute (offline) a function mapping any PDE parameter, to the matrix of coefficients of optimal test functions (in some basis expansion) associated with that PDE parameter. Next, as a remedy for the second shortcoming, we use the low-rank approximation to hierarchically compress the (non-square) matrix of coefficients of optimal test functions. In order to accelerate this process, we train a neural network to learn a critical bottleneck of the compression algorithm (for a given set of PDE parameters). When solving online the resulting (compressed) Petrov–Galerkin formulation, we employ a GMRES iterative solver with inexpensive matrix–vector multiplications thanks to the low-rank features of the compressed matrix. We perform experiments showing that the full online procedure is as fast as an (unstable) Galerkin approach. We illustrate our findings by means of 2D–3D Eriksson–Johnson problems, together with 2D Helmholtz equation

Autonomic care platform for optimizing query performance

Background: As the amount of information in electronic health care systems increases, data operations get more complicated and time-consuming. Intensive Care platforms require a timely processing of data retrievals to guarantee the continuous display of recent data of patients. Physicians and nurses rely on this data for their decision making. Manual optimization of query executions has become difficult to handle due to the increased amount of queries across multiple sources. Hence, a more automated management is necessary to increase the performance of database queries. The autonomic computing paradigm promises an approach in which the system adapts itself and acts as self-managing entity, thereby limiting human interventions and taking actions. Despite the usage of autonomic control loops in network and software systems, this approach has not been applied so far for health information systems. Methods: We extend the COSARA architecture, an infection surveillance and antibiotic management service platform for the Intensive Care Unit (ICU), with self-managed components to increase the performance of data retrievals. We used real-life ICU COSARA queries to analyse slow performance and measure the impact of optimizations. Each day more than 2 million COSARA queries are executed. Three control loops, which monitor the executions and take action, have been proposed: reactive, deliberative and reflective control loops. We focus on improvements of the execution time of microbiology queries directly related to the visual displays of patients' data on the bedside screens. Results: The results show that autonomic control loops are beneficial for the optimizations in the data executions in the ICU. The application of reactive control loop results in a reduction of 8.61% of the average execution time of microbiology results. The combined application of the reactive and deliberative control loop results in an average query time reduction of 10.92% and the combination of reactive, deliberative and reflective control loops provides a reduction of 13.04%. Conclusions: We found that by controlled reduction of queries' executions the performance for the end-user can be improved. The implementation of autonomic control loops in an existing health platform, COSARA, has a positive effect on the timely data visualization for the physician and nurse